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₹4800 were divided among P, Q and R, such that 6 times of P = 3 times of Q = 8 times of R. Find the share of R.
₹815
₹960
₹1034
₹1068
₹960
To solve this, we express the relationship as 6P = 3Q = 8R = k. This implies P = k/6, Q = k/3, and R = k/8. Given P + Q + R = 4800, we find the common denominator (24) to get 4k + 8k + 3k = 24 * 4800, resulting in 15k = 115200, which gives R = k/8 = 960.
To solve this, we express the relationship as 6P = 3Q = 8R = k. This implies P = k/6, Q = k/3, and R = k/8. Given P + Q + R = 4800, we find the common denominator (24) to get 4k + 8k + 3k = 24 * 4800, resulting in 15k = 115200, which gives R = k/8 = 960.
This problem involves the concept of Ratio and Proportion, a fundamental topic in Quantitative Aptitude often used in calculating Financial Allocation in the Indian Economy, such as the distribution of the Divisible Pool of Taxes between the Centre and States as per Finance Commission recommendations (Article 280).
The total sum is divided based on the inverse ratio of the given coefficients.
The ratio P:Q:R is 4:8:3, derived from 1/6 : 1/3 : 1/8.
The sum of ratio parts (4+8+3=15) corresponds to the total amount of ₹4800.
P's share is (4/15) * 4800 = ₹1280.
Q's share is (8/15) * 4800 = ₹2560.
Option B (₹960) is the correct share for R, calculated as (3/15) of 4800.
B is correct — The share of R in the total amount of ₹4800 is ₹960.
Understanding ratio distribution is essential for solving problems related to Partnership (Business) and Mixture & Alligation chapters in SSC and Banking exams.
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