CTET Math Question Papers 2018

CTET Math Question Papers 2018 - You can find here Question Papers of Mathematics for Central Teacher Eligibility Test (CTET) Examination to be held in July 2018 online.

1. Let A = (x + 1)/(x – 1 ) and B = (x – 1)/(x + 1). Determine the value of A – B
a. 0
b. x/(x² - 1)
c. 4x/(x² - 1)
d. None of these

2. Ashok had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product ?
a. 1050
c. 1440
d. none of these

3. A ladder on a road when inclined on a wall reaches a point 12 m above ground. Placing at the same position if it is inclined on to other side of a road, it reaches a point 9m above the ground. If the length of ladder is 15 m, what is the width of the road ?
a. 17 m
b. 23 m
c. 19 m
d. 21 m

4. The rate of interest on two bonds is in the ratio of 4 : 5. A person wants to invest his savings in these bonds in such a way that he received equal half yearly interest from both the bonds. He should invest in these bonds in the ratio :
a. 5 : 2
b. 2 : 5
c. 4 : 5
d. 5 : 4

5. A student secured 60, 75 and 85 in Mathematics monthly test. If monthly scores were given equal weightage and final scores are given double weightage , what are his average marks in Mathematics ?
a. 65
b. 75
c. 80
d. None of these

6. A sells a product having a printed price of Rs.2,400 at a discount of 10% on printed price. He earns a profit of 25% in this sale. What was the purchase price on which A purchased this product ?
a. Rs.1980
b. Rs.1728
c. Rs.2160
d. Rs.1800

7. A wheel travels a distance of 22 km in 2500 revolutions. Find the diameter of the wheel.
a. 1.4 m
b. 2.8 m
c. 5.6 m
d. None of these

8. The difference between the compound interest and simple interest on a sum of money at the rate of 10% p.a. for 2 years is Rs.50. Find the principal amount.
a. Rs.5,500
b. Rs.4,000
c. Rs.5,000
d. None of these

9. If the numerator of a fraction is doubled and the denominator is increased by 3, the new fraction is 3/5. What is the original fraction if its denominator is more than twice the numerator by 1 ?
a. 3/7
b. 6/13
c. 1/3
d. 5/11

10. Three taps A, B and C can fill the tank in 30 minutes, 45 minutes and 60 minutes respectively. All the three taps are opened simultaneously and after 10 minutes, tap C is closed and another tap D is opened. It took another 20 minutes to fill the tank. How much time does tap D take to empty a full tank ?
a. 18 minutes
b. 24 minutes
c. 30 minutes
d. 36 minutes

11. A rod of length 300 inches is to be cut into three pieces of integer length such that length of the first piece is square of the second and that of the second is square of the third. What is the length of the left out portion, if the left out portion has to be the least ?
a. 12 inches
b. 24 inches
c. 8 inches
d. 30 inches

12. The amount on a certain sum for 3 and 4 years at a certain rate of compound interest are Rs.18250.50 and Rs.20988.10 respectively. What is the rate of interest ?
a. 10%
b. 12%
c. 13%
d. None of these

13. The difference between simple interest and compound interest on a certain sum of money for 2 years at 10% p.a. is Rs.4200. The sum is :
a. Rs.20,000
b. Rs.16,000
c. Rs.24,000
d. None of these

14. In an examination A gets 40% of total marks and B gets 80% of that of A. C gets 60% of A’s and B’s marks taken together. D gets 45% of A’s and C’s marks taken together. If the required pass percentage is 36, how many of these four students passed the examination ?
a. 1
b. 2
c. 3
d. 4
15. In a school, the number of girls exceeds the number of boys by 60. If the number of girls is increased by 15% and the number o boys is increased by 50%, there would be 15 boys more than girls. Find the original strength of the class ?
a. 540
b. 360
c. 720
d. 600

16. An investor invested a sum of Rs.10 lakhs in shares of company X and of company Y. Company X’s share yields 24% in cash each year and the rate of interest on company Y’s debentures is 16%. He received a total of Rs.2,08,000 in the form of dividend and interest from these two companies. How much money was invested in company X ?
a. 400000
b. 600000
c. 650000
d. None of these

17. A dry fruit seller purchased 3 kinds of nuts at the rate of Rs.100/kg, Rs.80/kg and Rs.60/kg respectively. He then mixed them in the ratio of 3 : 4 : 5 by weight and sold the same to a customer at 50% profit. The price per kg at which he sold the mix to the customer is :
a. Rs.110
b. Rs.90
c. Rs.70
d. None of these

18. A, B and C were partners sharing profits in the ratio of 2 : 3 : 4 : 6. D died and his share was distributed equally among the surviving partners. What will be the new profits sharing ratio ?
a. 4 : 5 : 6
b. 2 : 3 : 4
c. 3 : 4 : 5
d. None of these

19. A vehicle changed hands 3 times and at each time the loss to the earlier owner was 10%. If the overall loss was Rs.4,065, find the original price of the vehicle (in rupees).
a. 10,000
b. 10,500
c. 15,000
d. 5,000

20. What is the three digit number which is a 2 more than a perfect square and 2 less than a perfect cube ?
a. 627
b. 402
c. 123
d. None of these

21. If it costs Rs.Y to whitewash the 4 walls of a room, how much would it cost(in rupees), if all the dimensions were to be 5 times the original dimensions ?
a. 5 Y
b. 25 Y
c. 25 Y²
d. 20 Y

22. A sum of Rs.4000 was lent partly at 6% and partly at 8% simple interest. If the interest received after one year is Rs.272, find the ratio in which the money was lent.
a. 2 : 3
b. 3 : 2
c. 1 : 2
d. None of these

23. A man pays off 3/20 of his debt every month . At the end of 6 months, his remaining debt is Rs.290. How much amount (in rupees) has he cleared off every month ?
a. 400
b. 435
c. 450
d. 500

24. Y wanted to borrow Rs.1000 from a moneylender for a period of one year. However, the moneylender deducted Rs.200 as interest charges and gave Rs.800 to him. What is the rate of interest at which Y has borrowed the money ?
a. 20%
b. 22.5%
c. 25%
d. 27.5%

25. If the interest compounded annually on a certain sum at a certain rate of interest for 2 years is equal to 55% of the simple interest on the same amount at the same rate of interestfor twice the time period, find the rate of interest.
a. 12%
b. 20%
c. 24%
d. None of these

1. c 2. b 3. d 4. d 5. d
6. b 7. b 8. c 9. a 10. b
11. b 12. d 13. d 14. c 15. a
16. b 17. d 18. a 19. c 20. c
21. b 22. b 23. b 24. c 25. b

1. The diagonal of a square is 4v 2 cm. The diagonal of another square whose area is double that of the first square is—
(A) 8 cm
(B) 8v2 cm
(C) 4v 2 cm
(D) 16 cm
Ans : (A)
2. A train starts with the speed of 70 km/hr with its speed increasing every two hours by 10 km/hr. In how many hours will it cover 345 kms ?
(A) 2¼ hrs
(B) 4 hrs 5 mins
(C) 4½ hrs
(D) None of the above
Ans : (C)
3. How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length ?
(A) 9•8 sec
(B) 12•1 sec
(C) 12•42 sec
(D) 14•3 sec
Ans : (B)
4. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water ?
(A) 40 mins
(B) 1 hr
(C) 1 hr 15 mins
(D) 1 hr 30 mins
Ans : (C)
6. The ratio of the incomes of A and B is 5 : 4 and the ratio of their expenditure is 3 : 2. If at the end of each year, each saves Rs. 1600, then the income of A is—
(A) Rs. 3400
(B) Rs. 3600
(C) Rs. 4000
(D) Rs. 4400
Ans : (C)
7. Half of 1 per cent is equal to—
(A) 0•005
(B) 0•05
(C) 0•02
(D) 0•2
Ans : (A)
8. If 3/5th of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it ?
(A) 40 sec
(B) 30 sec
(C) 36 sec
(D) 24 sec
Ans : (A)
9. In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth Rs. 8 per litre ?
(A) 1 : 2
(B) 2 : 1
(C) 2 : 3
(D) 3 : 2
Ans : (A)
10. A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is—
(A) 214
(B) 476
(C) 954
(D) 1908
Ans : (A)
11. The difference between simple and compound interest @ 10% per annum on a sum of Rs. 1000 after 4 years is—
(A) Rs. 31
(B) Rs. 32•10
(C) Rs. 40•40
(D) Rs. 64•10
Ans : (D)
12. The maximum length of a pencil that can by kept in a rectangular box of dimensions 8 cm × 6 cm × 2 cm, is—
(A) 2v13 cm
(B) 2v14 cm
(C) 2v26 cm
(D) 10v2 cm
Ans : (C)
13. What is the smallest number by which 3600 be divided to make it a perfect cube ?
(A) 9
(B) 450
(C) 50
(D) 300
Ans : (B)
14. At what time between 9 and 10 o’clock will the hands of a watch be together ?
(A) 45 min past 9
(B) 50 min past 9
(C) 49 1/11 min past 9
(D) 48 2/11 min past 9
Ans : (C)
15. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the number is reversed. The number is—
(A) 18
(B) 42
(C) 81
(D) 24
Ans : (D)
16. The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2 . The volume of the cuboid is—
(A) 24 cm3
(B) 48 cm3
(C) 64 cm3
(D) 120 cm3
Ans : (B)
17. In a school 10% of the boys are same in number as ¼ th of the girls. What is the ratio of boys to girls in the school ?
(A) 3 : 2
(B) 5 : 2
(C) 2 : 1
(D) 4 : 3
Ans : (B)
18. X got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price she bought. What was the labelled price ?
(A) Rs. 16,000
(B) Rs. 12,000
(C) Rs. 10,000
(D) None of the above
Ans : (C)
19. A vendor loses the selling price of 4 oranges on selling 36 oranges. Her loss per cent is—
(A) 10%
(B) 11 1/9 %
(C) 12 ½ %
(D) None of the above
Ans : (A)
20. In a camp, 95 men had provisions for 200 days. After 5 days, 30 men left the camp. For how many days will the remaining food last now ?
(A) 180
(B) 285
(C) 139 16/19
(D) 28•5
Ans : (B)
21. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds in terms of ratio of their speed.
(A) Dog’s speed : hare’s speed = 15 : 16
(B) Dog’s speed : hare’s speed = 16 : 15
(C) Dog’s speed : hare’s speed = 3 : 5
(D) Dog’s speed : hare’s speed = 5 : 3
Ans : (B)
22. The ratio of the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is—
(A) 70 km/hr
(B) 75 km/hr
(C) 84 km/hr
(D) 87•5 km/hr
Ans : (D)
23. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is—
(B) 19 years
(C) 49 years
(D) 39 years
Ans : (D)
24. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in—
(A) 6 hours
(B) 6 2/3 hours
(C) 7 hours
(D) 7 ½ hours
Ans : (C)
25. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)—
(A) 20, 35, 45
(B) 8, 20, 28
(C) 16, 28, 36
(D) 20, 36, 46
Ans : (C)
1. A student gets an aggregate of 60% marks in five subjects in the ratio 10: 9: 8: 7: 6. If the passing marks are 50% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam?
(a) 2     (b) 3     (c) 4     (d) 5
2 P, Q and R are three consecutive odd numbers in ascending order. If the value of threetimes P is three less than two times R, find the value of R.
(a) 5 (b) 7 (c) 9 (d) 11
3. If log2[log7(x2 - x + 37) ] = 1, then what could be the value of x?
(a) 3 (b) 5 (c) 4 (d) None of these
4. After a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentabove the cost price does he mark his goods?
(a) 28.56% (b) 35% (c) 22.22% (d) None of these
5. An old man has Rs. (1! + 2! + 3! + ...+ 50!), all of which he wants to divide equally(Without fractions) among his n children. Then, n may be
(a) 5 (b) 7 (c) 9 (d) 11
6. A dealer buys dry fruit at Rs.100, Rs. 80 and Rs. 60 per kg. He mixes them in the ratio 3: 4: 5 by weight, and sells them at a profit of 50%. At what price does he sell the dry fruit?
(a) Rs. 80/kg (b) Rs. 100/kg (c) Rs. 95/kg (d) None of these
7. An express train travelling at 80 kmph overtakes a goods train, twice as long and goingat 40 kmph on a parallel track, in 54 seconds. How long will the express train take to cross a station 400 m long?
(a) 36 sec (b) 45 sec (c) 27 sec (d) None of these
8. A student, instead of finding the value of 7/8th of a number, found the value of 7/18th ofthe number. If his answer differed from the actual one by 770, find the number.
(a) 1584 (b) 2520 (c) 1728 (d) 1656
9. P and Q are two integers such that P ? Q = 64. Which of the following cannot be the value of P + Q?
(a) 20 (b) 65 (c) 16 (d) 35
10. The average marks of a student in ten papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.
(a) 55 (b) 60 (c) 62 (d) Cannot be determined.
11. If the roots, x1, and x2, of the quadratic equation x2 - 2x + c = 0 also satisfy the equation   7x2 - 4x1 = 47, then which of the following is true?
(a) c = - 15                                         (b) x1 = - 5, x2 = 3
(c) x1 = 4.5, x2 = - 2.5                       (d) None of these
12. The sum of the areas of two circles which touch each other externally is 153?. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.
(a) 4 (b) 2 (c) 3 (d) None of these
13. If m and n are integers divisible by 5, which of the following is not necessarily true?
(a) m - n is divisible by 5.             (b) m2 - n2 is divisible by 25.
(c) m + n is divisible by 10          (d) None of the above.
14. Which of the following is true?
(a) 7³² = (73)² (b) 7³² > (73)2 (c) 7³² < (73)2 (d) None of these
15. A man earns x% on the first 2000 rupees and y% on the rest of his income. If he earns Rs 700 from Rs 4000 and Rs 900 from Rs 5000 of income, find x.
(a) 20 (b) 15 (c) 35 (d) None of these
1. (c) 2. (b) 3. (c) 4. (a) 5. (c) 6. (d) 7. (c) 8. (a) 9. (d) 10. (b) 11. (a) 12. (a) 13. (c) 14. (b) 15. (b)

Complete the following statements using the help box:
1. The comparison of two quantities of the same kind by means of division is termed as ____.
2. The two quantities to be compared are called the ________ of the ratio.
3. The first term of the ratio is called the _________ and the second term is called the _______.
4. In a ratio, only two quantities of the __________ unit can be compared.
5. If the terms of the ratio have common factors, we can reduce it to its lowest terms by cancelling the
6. When both the terms of a ratio are multiplied or divided by the same number (other than zero) the
ratio remains _________ .The obtained ratios are called__________.
7. In a ratio the order of the terms is very important. (Say True or False)
8. Ratios are mere numbers. Hence units are not needed. (Say True or False)
9. Equality of two ratios is called a __________. If a,b;c,are in proportion, thena:b::c:.
10. In a proportion, the product of extremes =___________
Help Box:
1) Ratio 2) terms 3) antecedent, consequent 4) same 5) common terms 6) unchanged, equivalent ratios
7) True 8) True 9) proportion 10) product of means
1. Find 5 equivalent ratios of 2:7
2. Reduce 270 : 378 to its lowest term.
3. Find the ratio of 9 months to 1 year
4. If a class has 60 students and the ratio of boys to girls is 2:1, find the number of boys and girls.
5. A ribbon is cut into 3 pieces in the ratio 3: 2: 7. If the total length of the ribbon is 24 m, find the length
of each piece.
6. The ratio of boys to girls in a class is 4 : 5. If the number of boys is 20, find the number of girls.
7. If A : B = 4 : 6, B : C = 18 : 5, find the ratio of A : B : C.
8. A bronze statue is made of copper, tin and lead metals. It has1/10 of tin , 1/4of lead and the rest
copper. Find the part of copper in the bronze statue.
7th Direct variation and indirect variation
In direct variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is also
changed in the same ratio. Then x/ y = constant
In Indirect variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is do
not changed in the same ratio. Then xy = constant
Þ It can be stated that if two quantities vary inversely, their product is a constant
1. Choose the correct answer
i) If the cost of 8 kgs of rice is Rs 160, then the cost of 18 kgs of rice is
(A) Rs.480 (B) Rs 180 (C) Rs 360 (D) Rs 1280
ii) If the cost of 7 mangoes is `35, then the cost of 15 mangoes is
(A) Rs 75 (B) Rs 25 (C) Rs 35 (D) Rs 50
iii) A train covers a distance of 195 km in 3 hrs. At the same speed, the distance travelled in 5 hours is
(A) 195 km. (B) 325 km. (C) 390 km. (D) 975 km.
iv) If 8 workers can complete a work in 24 days, then 24 workers can complete the same work in
(A) 8 days (B) 16 days (C) 12 days (D) 24 days
v) If 18 men can do a work in 20 days, then 24 men can do this work in
(A) 20 days (B) 22 days (C) 21 days (D) 15 days
1. If varies directly as y, complete the given tables:
2. If varies inversely as y, complete the given tables:
3. A car travels 360 km in 4 hrs. Find the distance it covers in 6 hours 30 mins at the same speed
4. 7 men can complete a work in 52 days. In how many days will 13 men finish the same work?
5. A book contains 120 pages. Each page has 35 lines . How many pages will the book contain if every
page has 24 lines per page?
6. A car travels 60 km in 45 minutes. At the same rate, how many kilo metres will it travel in one hour?
7. A car takes 5 hours to cover a particular distance at a uniform speed of 60 km / hr. How long will it take to cover the same distance at a uniform speed of 40 km / hr?
8. 150 men can finish a piece of work in 12 days. How many days will 120 men take to finish the same work?
9. A troop has provisions for 276 soldiers for 20 days. How many soldiers leave the troop so that the provisions may last for 46 days?
10. A book has 70 pages with 30 lines of printed matter on each page. If each page is to have only 20 lines of printed matter, how many pages will the book have?
11. There are 800 soldiers in an army camp. There is enough provisions for them for 6o days. If 400 more soldiers join the camp, for how many days will the provisions last?
12. A wheel makes 48 revolutions in 3 seconds. How many revolutions does it make in 30 seconds?
7th Percentage
The word ‘Percent’ is derived from the Latin word ‘Percentum’, which means ‘per hundred’ or ‘hundredth’ or ‘out of 100’.
• Percentage also means ‘percent’.
• Symbol used for percent is %
• Any ratio 100 is called ‘Percent’.
1) Write the following as a percent: (i) 20:100 (ii) 100:93(iii)100/100 (iv)0.07
2) Write the following percent as a ratio: (i) 43% (ii) 17 1/2(iii) 5% (iv) 33 1/3 %
3) Write the following percent as a fraction: (i) 25% (ii) 12 1/2% 2 (iii) 33%
4) 9/10 of your blood is water. What % of your blood is not water.
5)  In a class of 35 students, 7 students were absent on a particular day. What percentages of the students were absent?
5. Ram bought 36 mangoes. 5 mangoes were rotten. What percentage of the mangoes was rotten?
6. In a class of 50, 23 were girls and the rest were boys. What is the percentage of girls and the percentage of boys?
7. Ravi got 66 marks out of 75 in Mathematics and 72 out of 80 in Science. In which subject did he score more?
8. Express as a decimal (a) 25.7% (b) 15%
9. Find the value of (a)% 1/2 of 200. (b) 0.75% of 40 kg.
10. In 2011, the population of a town is 1,50,000. If it is increased by 10% in the next year, fi nd the
population in 2012.
11. The percentage of literacy in a village is 47%. Find the number of illiterates in the village, if the population is 7,500.
12. Is it true? 20% of 25 is same as 25% of 20.
13. The tax in a restaurant is 1.5% of your total bill.
a) Write the tax % as a decimal.
b) A family of 6 members paid a bill of ` 750. What is the tax for their bill amount?
c) What is the total amount that they should pay at the restaurant?
14. Complete these
1) Any fraction with its denominator 100 is called __________
2)1/2 = -----------% 3) 35% = ------------ ( in fraction)
4) 0.05 = ----------------% 5)1/4 = ----- %
7th Profit and Loss

The price at which any one buys goods at the market is called the Cost Price(C.P.).
The price at which one can sell the goods at the market is called the Selling Price (S.P.).
Additional amount given or taken for CP is called the profit.
1. Choose the correct answer:
i) If the cost price of a bag is Rs. 575 and the selling price is Rs.625, then there is a profit of Rs.
(A) 50 (B) 575 (C) 625 (D) none of these
ii) If the cost price of the box is Rs.155 and the selling price is Rs.140, then there is a loss of Rs.
(A) 155 (B) 140 (C) 15 (D) none of these
iii) If the selling price of a bag is `235 and the cost price is `200, then there is a
(A) profit of Rs.235 (B) loss of Rs.3 (C) profit of Rs.35 (D) loss of Rs.200
iv) Gain or loss percent is always calculated on
(A) cost price (B) selling price (C) gain (D) loss
v) If a man makes a profit of Rs.25 on a purchase of Rs.250, then profit% is
(A) 25 (B) 10 (C) 250 (D) 225
1. Sanjay bought a bicycle for Rs. 5,000. He sold it for Rs.600 less after two years. Find the selling price and the loss percent.
2. A fruit seller bought 8 boxes of grapes at Rs.150 each. One box was damaged. He sold the remaining boxes at Rs.190 each. Find the profit / loss percent.
3. A shop keeper bought 10 bananas for `100. 2 bananas were rotten. He sold the remaining bananas at the rate of Rs. 11 per banana. Find his gain or loss % 6. A shop keeper purchased 100 ball pens for Rs. 250. He sold each pen for Rs. 4. Find the profit percent.
7. A vegetable vendor bought 40 kg of onions for Rs. 360. He sold 36 kg at Rs. 11 perkg. The rest were sold at Rs. 4.50 per kg as they were not very good. Find his profit / loss Percent.
8. A trader mixes two kinds of oil, one costing Rs. 100 per Kg. and the other costing `80 per Kg. in the ratio 3: 2 and sells the mixture at Rs. 101.20 per Kg. find his profit or loss percent.
9. Sathish sold a camera to Rajesh at a profit of 10 %. Rajesh sold it to John at a loss of 12 %. If John paid Rs. 4,840, at what price did Sathish buy the camera?
10. The profit earned by a book seller by selling a book at a profit of 5% is Rs. 15 more than when he
sells it at a loss of 5%. Find the Cost Price of the book.
7th Simple Interest
1. Radhika invested Rs.5,000 for 2 years at 11 % per annum. Find the simple interest and the amount received by him at the end of 2 years.
2. Find the simple interest and the amount due on Rs. 7,500 at 8 % per annum for 1 year 6 months.
3. Find the simple interest and the amount due on Rs. 6,750 for 219 days at 10 % per annum.
4. Rahul borrowed Rs. 4,000 on 7th of June 2006 and returned it on 19th August2006. Find the amount he paid, if the interest is calculated at 5 % per annum
5. Find the rate percent per annum when a principal of Rs. 7,000 earns a S.I. of Rs.1, 680 in 16 months.
6. Vijay invested Rs.10, 000 at the rate of 5 % simple interest per annum. He received Rs.11, 000 after some years. Find the number of years.
7. A sum of money triples itself at 8 % per annum over a certain time. Find the number of years.
8. A certain sum of money amounts to Rs.10, 080 in 5 years at 8 %. Find the principal
9. A certain sum of money amounts to Rs. 8,880 in 6 years and Rs. 7,920 in 4 years respectively. Find the principal and rate percent.
10. Find the principal that earns `250 as S.I. in 21/years at 10 % per annum.
11. In how many years will a sum of Rs. 5,000 amount to Rs.5,800 at the rate of 8 % per annum.
12. A sum of money doubles itself in 10 years. Find the rate of interest.
13. A sum of money doubles itself at 121/2 % per annum over a certain period of time. Find the number of years.
14. A certain sum of money amounts to Rs. 6,372 in 3 years at 6 % Find the principal.
15. A certain sum of money amounts to Rs. 6,500 in 3 years and Rs. 5,750 in 11/2years respectively. Find the principal and the rate percent?
16. Find the rate per cent at which, a sum of money becomes 9/4 times in 2 years.
17) If Ram needs Rs. 6, 00,000 after 10 years, how much should he invest now in a bank if the bank pays 20 % interest p.a?

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