Pinku, Rinku, and Tinku divide ₹4200 in the ratio 7 : 8 : 6. If ₹200 is added to each person’s share, what is the new ratio of their amounts?

Introduction / Context:
This question mixes proportional division and then a fixed increment to each share. First compute actual shares using the original ratio, then add the constant and reduce to the simplest ratio.

Given Data / Assumptions:

• Total = ₹4200; ratio = 7 : 8 : 6.
• Constant addition = ₹200 to each share.

Concept / Approach:
Convert the ratio into actual rupee amounts by dividing the total proportionally. Then apply the same increment to all three and finally reduce the triplet to a simplest ratio by dividing by any common factor.

Step-by-Step Solution:
Sum of parts = 7 + 8 + 6 = 21Value of 1 part = 4200 / 21 = ₹200Original shares: Pinku = 7*200 = ₹1400; Rinku = 8*200 = ₹1600; Tinku = 6*200 = ₹1200After adding ₹200 each: 1600, 1800, 1400New ratio = 1600 : 1800 : 1400 = 16 : 18 : 14 = 8 : 9 : 7

Verification / Alternative check:
The common factor 200 divides all three augmented shares, confirming 8 : 9 : 7.

Why Other Options Are Wrong:
8 : 9 : 5 and 7 : 9 : 5 do not reflect the equal increment effect. 7 : 8 : 6 is the original, not the updated ratio.

Common Pitfalls:
Adding ₹200 to the ratio numbers directly. Ratios must be converted to actual values before adding constants.

Final Answer:
8 : 9 : 7