Algebra Qb

Algebra | 1

Algebra 1. A number added to two-seventh of its value is equal to 72. Find the number.

a. 42

b. 56

c. 49

d. 35

2. The sum of four consecutive odd numbers is 80. Find the average of the four numbers.

a. 20

b. 10

c. 15

d. 18

3. What is the sum of two consecutive multiples of 3, the difference of whose squares is 81?

a. 15

b. 24

c. 27

d. 51

4. The sum of two numbers is 50. The fraction obtained by dividing the larger number by the smaller 3 number is . Find the numbers. 2

a. 20, 30

b. 15, 35

c. 24, 26

d. None of these

5. Six years ago, Sushil’s age was thrice that of Snehal’s age. Six years later, Sushil’s age will be

5 3

times the age of Snehal. What is the present age of Snehal?

a. 16

b. 14

c. 12

d. 18

6. The sum of the digits of a two digit number is 9 less than the number. Find the digit in the ten’s place of the number.

a. 4

b. 3

c. 2

d. 1

7. 33 pencils and 47 erasers together cost Rs. 299, while 47 pencils and 33 erasers cost Rs. 341. Find the cost of purchasing one pencil and one pen.

a. 8

b. 10

c. 12

d. 14

8. Four computers and three printers together cost Rs. 94,000, while six computers and eight printers cost Rs. 1,62,000. Find the cost of one computer.

a. 20,000

b. 19,000

c. 18,000

d. 21,000

9. In a two digit number, the digit in unit’s place is 1 more than twice the digit in ten’s place. If the digit in the unit’s and ten’s place is interchanged, we get a number which is 1 less than twice the original number. Find the number.

a. 49

b. 25

c. 37

d. 73

10 There are two numbers such that the sum of twice the first and thrice the second is 39 whereas the sum of thrice the first and twice the second is 36. Find the larger number.

a. 6

b. 9

c. 12

d. 8

11. The difference between a two digit number and the number obtained by interchanging the positions of the digits is 36. What is the difference between the two digits of the number?

a. 4

b. 6

c. 12

d. 5

12. The number obtained on interchanging the positions of the digits of a two digit number is 18 more than the original number. If the sum of the digits is 8, find the number.

a. 35

b. 53

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c. 27

d. 72

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2 | Algebra

13. The difference between two number is 642. When the larger number is divided by the smaller number, the quotient is 8 and the remainder is 19. Find the larger number.

a. 731

b. 273

c. 137

d. 89

14. Solve for p and q: 3(2p + q) = 7pq and 3(p + 3q) = 11pq.

a. 3/2, 1

b. 1, 4/3

c. 1, 3/2

d. 4/3, 1

15. In a given fraction, if the numerator is increased by 3 and the denominator is reduced by 3, the resulting fraction is 5/6. But if the numerator is increased by 4 and denominator is decreased by 4, the resulting fraction is 6/5. Find the original fraction.

a. 3/5

b. 5/9

c. 2/9

d. 1/7

16. For what value of k would the system of equation have infinite solutions: 12x – 20y = 32 and 15x – 25y = k.

a. 40

b. 44

c. 48

d. 56

c. 5 or 9

d. None of these

17. Find the solution to (x – 5)2 = 4(x – 5)

a. 5

b. 9

18. A packet of goods costs Rs. 360. If the quantity in the packet was 6 kgs more and the rate per kg had been Rs. 3 less, the total cost would still have been 360. How many kgs did the original packet contain?

a. 30

b. 24

c. 15

d. 18

19. 23 is divided into two parts such that the difference between the squares of each part is 23. Find the two parts.

a. 8, 15

b. 10, 13

c. 12, 11

d. 9, 14

20. For what value of c would the roots of the equation x –6x + c = 0 be real? 2



a. c ≤ 6

b. 3 ≥ c

c. c ≤ 9

d. c ≥ 9

21. For what value of k would the roots of the equation (k – 1)x2 + (2k + 2)x + k = 0 be equal?

a. 1

22. Find the value of 1 +



a.

1± 5 2

b. 1/3 1 1+

1

1+

1 1 + ......

b.

1+ 5 2

c. – 1/3

d. None of these

.

c.

1− 5 2

d.

1+ 3 2

23. If one root of the equation x2 – bx – 8 = 0 is square of the other root, find the value of b?

a. 2

b. 6

c. 8

d. 10

24. If the roots of the equation x2 – 3x + 4 = 0 is p and q, find the equation whose roots are (p + 2) and (q + 2).

a. x2 – 7x + 14

b. x2 – 7x + 12

c. x2 + 7x – 14

d. x2 + 7x – 12

25. Find the sum of first 35 terms of the series: 51 + 48 + 45 +……….

a. 102

b. 0

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c. 84

d. 92

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Algebra | 3

26. Find the number of terms in the following series: 7 + 14 + 21 + 28 + ………… + 147

a. 20

b. 22

c. 21

d. 23

27. Find the 100th term of the sequence 14, 18, 22, 26, ……..

a. 400

b. 410

c. 200

d. 205

28. If the 5th term of an A.P. is 8 and 7th term is 16, find the 13th term of the same series?

a. 24

b. 26

c. 40

d. None of these

29. Find the sum of first 15 terms of an A.P. whose 6 and 10 terms are 10 and 6 respectively. th



a. 120

b. 125

th

c. 140

d. 150

c. 2400

d. 1000

30. What is the sum of first 50 odd numbers?

a. 1200

b. 2500

31. If in a G.P., the sixth term is −

a. 27

1 1 and the ninth term is , find the first term? 9 243

b. 9

c. 18

d. 24

32. Find the sum of the infinite G.P. 90, 60, 40, ………

a. 180

b. 270

c. 900

33. If the first term of a G.P. is 120 and the common ratio is

a. 205/8

b. 20

d. 360 3 , then find the 4th term of this series. 4

c. 405/8

34. If the 8th and 10th terms of the geometric series are

d. 50

1 1 and respectively, then find the first term 32 128

of the series.

a. 2

b. 4

c. 8

d. 16

35. The 11th and 17th terms of an A.P. are 11 and 8 respectively. Starting with the first term, how many terms of the series need to be added such that the sum is 231.

a. 12

b. 35

c. 77

d. 70

36. E1 is an equilateral triangle whose area is 16 sq. cm. The mid-points of the sides of the triangle are joined to form another triangle E2. The mid-points of the sides of E2 are joined to form another triangle E3 and the process is repeated infinite times. Find the sum of the areas of all triangles E1, E2, E 3, …

a. 32

b. 64/3

c. 64

d. None of these

37. On being asked her age, a girl says “my age five years from now would be 1.5 times my age five years back”. What will be her age ten years from now?

a. 20 years

b. 35 years

c. 25 years

d. 30 years

38. A third of Raju’s marks in Math exceeds a half of his marks in English by 30. If his total score in both the subjects is 240, his marks in Math and English are:

a. 60, 180

b. 180, 60

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c. 200, 160

d. 160, 200

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4 | Algebra

39. A shopkeeper sell half of the rice with him and donates half a kilo. He again sells half the remaining rice and donates half a kilo. Now he has no rice left in his store. How much rice did he have in his store initially?

a. 4 kg

b. 3 kg

c. 5 kg

d. 2 kg

40. In a parking lot of a park, there are either 3 wheelers or 8 wheelers. If there are 100 vehicles in all and 500 wheels, then how many three wheelers are there?

a. 60

b. 40

c. 80

d. 70

41. If two pencils and 3 pens cost Rs. 19 and 5 pens and 3 pencils cost Rs. 21, what is the price of 5 pencils and 8 pens?

a. Rs. 25

b. Rs. 30

c. Rs. 35

d. Rs. 40

42. An employer pays Rs. 20 for each day of work and forfeits Rs. 3 for each idle day spent. At the end of 60 days, a worker gets Rs. 280. For how many days was the worker?

a. 30

b. 20

c. 40

d. 15

43. A total sum of Rs. T was to be given to 18 workers but 4 of which did not turn up for collecting their share of salary. Hence the extra amount left over was distributed equally among the others, thereby increasing their salaries by Rs. 80. What is the value of T?

a. 5000

b. 5040

c. 2060

d. 3080

44. The difference between a two digit number and the number formed by reversing the two digits is 27. Which of the following can be the product of the two digits?

a. 8

b. 10

c. 7

d. none of these

45. If from a positive natural number, we subtract 4 times its reciprocal, the result is –3. What is the number?

a. –4

b. 1

c. 2

d. 4

46. If 4 times a positive number is subtracted from square of the natural number, the result is 21. What will be the result if a similar operation is done on a number two more than the earlier number?

a. 18

b. 16

c. 5

d. 45

Answer Key 1. b

2. a

3. c

4. a

5. c

6. d

7. a

8. b

9. c

10. b

11. a

12. a

13. a

14. c

15. c

16. a

17. c

18. b

19. c

20. c

21. c

22. b

23. a

24. a

25. b

26. c

27. b

28. c

29. a

30. b

31. a

32. b

33. c

34. b

35. c

36. b

37. b

38. b

39. b

40. a

41. d

42. c

43. b

44. b

45. b

46. d

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