Number System problems
- 1. The sum of two number is 29 and the difference of their squares is 145. The difference between the number is?
Options- A. 13
- B. 5
- C. 8
- D. 11 Discuss
Correct Answer: 5
Explanation:
Let the number be a and b
Then, (a-b) = (a2 - b2) / a+b
= 145/29
= 5
- 2. The difference of two number is 5 and the difference of their squares is 135. The sum of the number is?
Options- A. 27
- B. 25
- C. 30
- D. 32 Discuss
Correct Answer: 27
Explanation:
Let the number be a and b.
Then, (a + b) = (a2 -b2) / (a-b)
= 135/5
= 27
- 3. If 1 is added to the denominator of fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is?
Options- A. 4/7
- B. 5/9
- C. 2/3
- D. 10/11 Discuss
Correct Answer: 2/3
Explanation:
Let the required fraction be x/y
Then, x/(y + 1) = 1/2
? 2x - y = 1 ...(1)
(x + 1) / y = 1
? x - y = -1 ...(2)
Solving Eq. (1) and (2)
We get x = 2, y = 3
? The fraction is 2/3
- 4. 4/5 of a number exceeds its 2/3 by 8. The number is?
Options- A. 30
- B. 60
- C. 90
- D. None of these Discuss
Correct Answer: 60
Explanation:
Let the number be x,
Then, 4x/5 - 2x/3 = 8
? (12x - 10x) / 15 = 8
? 2x = 120
? x = 60
- 5. If one-fourth of one-third of one-half of a number is 15, the number is?
Options- A. 72
- B. 120
- C. 180
- D. 360 Discuss
Correct Answer: 360
Explanation:
Let the number be N .
Then, 1/4 of 1/3 of 1/2 of N = 15
? 1/4 x 1/3 x 1/2 x N = 15
? N/24 = 15
? N = 24 x 15 = 360 .
- 6. A number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is?
Options- A. 160
- B. 180
- C. 200
- D. 220 Discuss
Correct Answer: 200
Explanation:
Let the number be N.
Then, (N/5) + 5 = (N/4) - 5
? (N/4) - (N/5) = 10
? (5N - 4N)/20 = 10
? N = 200
- 7. The product of two numbers is 120. The sum of their squares is 289. The sum of the two numbers is?
Options- A. 20
- B. 23
- C. 169
- D. None of these Discuss
Correct Answer: 23
Explanation:
Let the number be a and b .
Then, (a+b)2 = a2 + b2 + 2ab
= 289 + 2 x 120
= 289 + 240
= 529
? a+b = ?529 = 23
- 8. The sum of squares of two numbers is 80 and the square of their difference is 36. The product of the two numbers is?
Options- A. 22
- B. 44
- C. 58
- D. 116 Discuss
Correct Answer: 22
Explanation:
Let the number be a and b.
Then, a2 + b2 = 80
and (a - b)2= 36
? a2 + b2 - 2ab = 36
? 2ab = (a2 + b2)-36
= 80 - 36= 44
? Product = ab = 22
- 9. The sum of two number is twice their difference, If one of the number is 10, the other number is?
Options- A. 31/ 3
- B. 30
- C. 1/3
- D. 41/ 4 Discuss
Correct Answer: 30
Explanation:
Let the other number be x.
Then, 10 + x = 2(x - 10)
? x = 30
- 10. 4/5 of a certain number is 64, Half of that number is?
Options- A. 32
- B. 40
- C. 80
- D. 16 Discuss
Correct Answer: 40
Explanation:
Let the number be N,
Then 4N/5 = 64
? N = 64 x 5/4 = 80
? Half of the number = 80/2 = 40
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