A sum of ₹ 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6. What is the difference between the maximum share and the minimum share?
- (a) ₹ 300
- (b) ₹ 350
- (c) ₹ 400 ✓ UPSC's answer
- (d) ₹ 450
Why the answer is (c)
• Convert the fractional ratio 1/2 : 3/4 : 5/6 to whole numbers by multiplying by the LCM of the denominators (12), resulting in 6 : 9 : 10.
• Calculate the total number of parts in the ratio: 6 + 9 + 10 = 25 parts.
• Determine the value of one part by dividing the total sum by the total parts: ₹ 2,500 / 25 = ₹ 100.
• Identify the maximum share (Z) as 10 parts and the minimum share (X) as 6 parts.
• Calculate the difference in parts: 10 - 6 = 4 parts.
• Multiply the difference in parts by the value of one part: 4 * ₹ 100 = ₹ 400, which corresponds to option (c).
Why the other options are wrong
- (a) ₹ 300
- ₹ 300 corresponds to a difference of 3 parts, which does not match the 4-part difference between the maximum and minimum shares.
- (b) ₹ 350
- ₹ 350 is not a multiple of the part value (₹ 100) and does not correspond to any integer difference in the ratio parts.
- (d) ₹ 450
- ₹ 450 corresponds to a difference of 4.5 parts, which is impossible as the ratio parts are integers.
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.