Simplification problems
- 1. How many 1/8's are there in 37 1/ 2?
Options- A. 300
- B. 400
- C. 500
- D. Cannot be determined Discuss
Correct Answer: 300
Explanation:
Number of 1/8 s = (75/2) / (1/8) = (75/2) x 8 = 300
- 2. 3/48 is what part of 1/12?
Options- A. 3/7
- B. 1/12
- C. 4/3
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let N of 1/12 = 3/48.
Then, N = 3/48 x 12 = 3/4
- 3. A boy was asked to multiply a given number by (8/17). Instead he divided the given number by (8/17) and got the result 225 more then what he should have got if he had multiplied the number by ( 8/17). The given number was?
Options- A. 8
- B. 17
- C. 64
- D. 136 Discuss
Correct Answer: 136
Explanation:
? N x 17/8 - N x 8/17 =225
? 225 x N / 136 = 225
? N = (225 x 136) / 225 = 136
- 4. In an examination, a student was asked to find (3/14) of a certain number, by mistake he found (3/4) of it. His answer was 150 more then the correct answer. The given number is?
Options- A. 180
- B. 240
- C. 280
- D. 290 Discuss
Correct Answer: 280
Explanation:
? 3N/4 - 3N/14 =150
? 15N/28 = 150
? N = (150 x 28) /15 = 280
- 5. If we multiply a fraction by itself and divided the product by its reciprocal, the fraction thus obtained is 18 26/ 27. The original fraction is?
Options- A. 8/27
- B. 22/3
- C. 11/3
- D. None of these Discuss
Correct Answer: 22/3
Explanation:
? N x N x 1/N = 1826/27
? N3 = 512/27
? N3= (8/3)3
? N = 8/3 = 22/3
- 6. The smallest fraction which should be subtracted from the sum of 1 3/ 4, 2 1/ 2, 5 7/ 12, 3 1/ 3 and 2 1/ 4 to make the result a whole number is?
Options- A. 5/12
- B. 7/12
- C. 1/2
- D. 7 Discuss
Correct Answer: 5/12
Explanation:
? 7/4 + 5/2 + 67/12 + 10 + 9/4 = (21 + 30 + 67 + 40 + 27/12) = 185/12
This is nearly greater than 15. Let required fraction be x.
Then, 185/12 - x = 15
? x = (185/12) - 15
= 5/12
- 7. Gopal was asked to find 7/9 of a fraction. But he made a mistake of dividing the given fraction by 7/9 and got an answer which exceeded the correct answer by 8/21. The correct answer is?
Options- A. 3/7
- B. 7/12
- C. 2/21
- D. 1/3 Discuss
Correct Answer: 7/12
Explanation:
? Let the fraction = N
? (9 x N)/7 - (7 x N)/9 = 8/21
? (32 x N)/63 = 8/21
? N = (8/21) x (63/32) = 3/4
? Correct answer = N x 7/9 = 7/9 x 3/4 = 7/12
- 8. The highest score in an innings was 3/11 of the total and the next highest was 3/11 of the remainder. If the scores differed by 9, then the total score is?
Options- A. 99
- B. 110
- C. 121
- D. 132 Discuss
Correct Answer: 121
Explanation:
Let total score be N.
Then highest score = 3N/11
Remainder = (N - 3N/11) = 8N/11
Next highest score = 3/11 of 8N/11 = 24N/121
Now, ? 3N/11 - 24N/121 = 9
? 9N/121 = 9
?N = 121
- 9. In a family, the father took 1/4 of the cake and he had 3 times as much as others had. The total number of family members is?
Options- A. 3
- B. 7
- C. 10
- D. 12 Discuss
Correct Answer: 10
Explanation:
Let there be N members, other than father .
Father's share = 1/4, other's share = 3/4.
Each of other's share = 3/4N
? 3 x 3/4N = 1/4
? N = 9
Hence, the total number of members = N + 1 = 10
- 10. Ravi earns twice as much in January as in each of the other months. What part of his annual earnings he earns in that month?
Options- A. 2/13
- B. 1/10
- C. 5/7
- D. 1/5 Discuss
Correct Answer: 2/13
Explanation:
Suppose Ravi earns Rs. N in each of the 11 months.
Then earning in January = Rs. 2 x N.
? Total annual income = (11 x N + 2 x N) = Rs. 13 x N
Part of total earning in January = (2 x N) / (13 x N) = 2/13
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