Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?

(a) 2/3
(b) 3/4
(c) 4/5
(d) 5/6 ✓ UPSC's answer

Why the answer is (d)

• For a fraction a/b, adding 5 to both numerator and denominator gives (a+5)/(b+5), so the change is (a+5)/(b+5) - a/b.

• For 2/3: 7/8 - 2/3 = 5/24.

• For 3/4: 8/9 - 3/4 = 5/36.

• For 4/5: 9/10 - 4/5 = 1/10 = 5/50.

• For 5/6: 10/11 - 5/6 = 5/66, which is smaller than 5/24, 5/36, and 5/50, so option (d) 5/6 has the minimum change.

Why the other options are wrong

(a) 2/3: 2/3 changes by 5/24, which is larger than the 5/66 change for 5/6.
(b) 3/4: 3/4 changes by 5/36, which is larger than the 5/66 change for 5/6.
(c) 4/5: 4/5 changes by 1/10, which is larger than the 5/66 change for 5/6.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.