Number System
- A candidate in an examination was asked to find 5/14 of a certain number. By mistake he found 5/14 of it. Thus, his answer was 25 more than the correct answer. The number was :
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Let us assume the required number be n.
As per given question,⇒ n × 5 − n × 5 = 25 4 14
Solve this equation further to get the answer.Correct Option: A
Let us assume the required number be n.
As per given question,⇒ n × 5 − n × 5 = 25 4 14 ⇒ 5n 
1 − 1 
= 25 4 14 ⇒ 5n 7 − 2 = 25 ⇒ 5n × 5 = 25 28 28 ⇒ n = 25 × 28 = 28 5 × 5
- 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 than the correct answer. The given number is :
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Let us assume the number is p.
According to given question,3 p − 3 p = 150 4 14 ⇒ 21p − 6p = 150 28
Solve this equation further to get the answer.
Correct Option: B
Let us assume the number is p.
According to given question,3 p − 3 p = 150 4 14 ⇒ 21p − 6p = 150 28
⇒ 15p = 28 × 150⇒ p = 28 × 150 = 280 15
- If a and b are two odd positive integers, by which of the following integers is (a4 – b4) always divisible ?
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We know that , a4 – b4 = (a2)2 – (b2)2 = (a2 + b2) (a2 − b2) = (a2 + b2) (a + b) (a – b)
Correct Option: C
We know that , a4 – b4 = (a2)2 – (b2)2 = (a2 + b2) (a2 − b2) = (a2 + b2) (a + b) (a – b)
Let a = 3, b = 1
∴ Required number = ( 3 + 1 ) ( 3 – 1 ) = 4 x 2 = 8
- If the difference between the reciprocal of a positive proper fraction and the fraction itself be 9/20 then the fraction is
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Let us assume that the fraction is P.
Therefore Reciprocal of the given fraction P = 1 . P
According to given question,P − = 9 1 P 20 Correct Option: C
The required fraction is 4 , 5 because 5 − 4 = 25 − 16 = 9 4 5 20 20
- Six numbers are arranged in decreasing order. The average of the first five numbers is 30 and the average of the last five numbers is 25. The difference of the first and the last numbers is :
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Let us assume that six numbers are p, q, r, s, t, u.
According to the given question, Numbers are in decreasing order :
p > q > r > s > t > u
Again according to the question,
p + q + r + s + t = 5 × 30
q + r + s + t + u = 5 × 25Correct Option: B
Let us assume that six numbers are p, q, r, s, t, u.
According to the given question, Numbers are in decreasing order :
p > q > r > s > t > u
Again according to the question,
p + q + r + s + t = 5 × 30
⇒ p + q + r + s + t = 150 --- (i)
q + r + s + t + u = 5 × 25
⇒ q + r + s + t + u = 125 --- (ii)
By equation (i) – (ii)
p – u = 150 – 125 = 25
