Problems on Numbers

1. When 15 is subtracted from 7 times the number, the result is 10 more than twice of the number. Find the number:
(a) 4        (b) 15
(c) 7.5      (d) 5

2. Sum of a rational number and its reciprocal is 13/6. Find the number:
(a) 2         (b) 3/2
(c) 4/2     (d) 5/2

3. The difference between a number and its 3/5 is 50. Find the number:
(a) 100    (b) 110
(c) 120    (d) 125

4. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
(a) 15     (b) 20
(c) 25     (d) 35

5. If one-third of one-fourth of a number is 15, then three-tenth of that number is:
(a) 34      (b) 44
(c) 54    (d) 64

6. A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number?
(a) 8      (b) 10
(c) 12      (d) 14

7. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
(a) 17      (b) 15
(c) 8       (d) 3

8. The product of two numbers is 120 and the sum of their squares is 289. The sum of the numbers is:
(a) 20    (b) 23
(c) 27    (d) 150

9. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
(a) 12    (b) 13
(c) 15   (d) 17

10. Find the number which when multiplied by 15 is increased by 196:
(a) 10      (b) 12
(c) 14    (d) 16

11. If the sum of 1/2 and 1/5 of a number exceeds 1/3 of the number by 7/3, then number is:
(a) 15    (b) 20
(c) 25   (d) 30

12. Product of two natural numbers is 17. The sum of reciprocals of their squares is:
(a) 128/9       (b) 290/289
(c) 290/90    (d) 290/19

13. Sum of three numbers is 264. If the first number is twice the second and third number is one-third of the first, the second number is:
(a) 72         (b) 73
(c) 74          (d) 75

14. Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is:
(a) 10:9     (b) 11:9
(c) 12:9     (d) 13:9

15. Two numbers differ by 5. If their product is 336, then sum of the two numbers is:
(a) 36       (b) 37
(c) 38       (d) 39

16. Difference between a two-digit number and the number obtained by interchanging the two digits is 36. What is the difference between two numbers?
(a) 4         (b) 6
(c) 8        (d) 12

17. Sum of two numbers is 25 and their difference is 13. Find their product:
(a) 108      (b) 114
(c) 124      (d) 134

18. A father is twice as old as his son. Twenty years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is:
(a) 44      (b) 54
(c) 64        (d) 74

19. Which among the following is not a prime number?
(a) 72        (b) 97
(c) 133      (d) 147

20. If 50 is subtracted from two-third of a number, the result is equal to sum of 40 and one-fourth of that number. Find the number:
(a) 210     (b) 214
(c) 216   (d) 234