The monthly salaries of A and B are in the ratio 15 : 16 and the monthly salaries of B and C are in the ratio 17 : 18. If the total of their monthly salaries together is Rs. 1,87,450, what is the monthly income of C?

Introduction / Context:
This question combines two ratio relationships and a total sum to find the individual salary of one person. We are given A : B and B : C and the total of A + B + C. From these, we need to derive A : B : C and then compute C's share. This type of chained ratio problem appears very frequently in aptitude exams and helps to test consistency in working with multiple related ratios.

Given Data / Assumptions:

• Ratio of salaries of A and B is 15 : 16.
• Ratio of salaries of B and C is 17 : 18.
• Total of salaries A + B + C = Rs. 1,87,450.
• We assume all salaries are positive and fixed for the calculation.

Concept / Approach:
We first convert the two given ratios into a single combined ratio A : B : C. Let A = 15x and B = 16x from the first ratio. From the second ratio, let B = 17y and C = 18y. Since B is common, we set 16x = 17y and express everything in one variable. This gives us A, B and C in a consistent ratio. After that, the total salary is used to find the actual monetary value of one ratio unit, and then C's salary is obtained by multiplying that unit value with C's ratio term.

Step-by-Step Solution:
From A : B = 15 : 16, let A = 15x and B = 16x.From B : C = 17 : 18, let B = 17y and C = 18y.Since both expressions represent B, set 16x = 17y.So y = 16x / 17.Now express C in terms of x: C = 18y = 18 * (16x / 17) = 288x / 17.Thus A : B : C = 15x : 16x : 288x / 17.Multiply each term by 17 to clear the denominator: 15x * 17 : 16x * 17 : 288x.This gives A : B : C = 255 : 272 : 288.Sum of ratio terms = 255 + 272 + 288 = 815.Total salary A + B + C = Rs. 1,87,450, so each unit = 187450 / 815 = 230.C's salary = 288 * 230 = Rs. 66,240.

Verification / Alternative check:
Compute A and B using the same unit value.A = 255 * 230 = Rs. 58,650.B = 272 * 230 = Rs. 62,560.Check total: 58,650 + 62,560 + 66,240 = 1,87,450, which matches the given total.Check ratios: A : B = 58,650 : 62,560 simplifies to 15 : 16, and B : C = 62,560 : 66,240 simplifies to 17 : 18.Thus all conditions are satisfied.

Why Other Options Are Wrong:
Other figures such as Rs. 72,100 or Rs. 62,200 do not conform to the derived ratio 255 : 272 : 288. If any of these were taken as C's salary, the implied values of A and B would either fail to add up to Rs. 1,87,450 or fail to maintain the given pairwise ratios. Only Rs. 66,240 fits perfectly with both the total and the ratio conditions.

Common Pitfalls:
Candidates sometimes combine A : B and B : C incorrectly and directly multiply all numbers, leading to a wrong three way ratio. Another error is to forget to align the common term B by using a common multiple. Always express the common term (here B) consistently, find A : B : C as a single ratio, then use the total to scale up to actual values.

Final Answer:
The monthly income of C is Rs. 66,240.