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₹3300 were divided among P, Q and R, such that 4 times of P = 7 times of Q = 2 times of R. Find the share of R.
₹2024
₹2028
₹2046
₹1848
₹1848
Find the ratio by taking the reciprocal of the coefficients (4, 7, 2). The ratio P:Q:R is (1/4):(1/7):(1/2) = 7:4:14. Total parts = 25. R's share = (14/25) × 3300.
Total amount = ₹3300. Ratio relationship: 4P = 7Q = 2R.
P:Q:R=a1:b1:c1 where aP=bQ=cR
Find the ratio by taking the reciprocal of the coefficients (4, 7, 2). The ratio P:Q:R is (1/4):(1/7):(1/2) = 7:4:14. Total parts = 25. R's share = (14/25) × 3300.
Many students mistake the ratio to be 4:7:2 instead of the reciprocal, or they fail to divide the total by the sum of ratio parts correctly.
Establish the Ratio
Given 4P=7Q=2R=k. Express variables in terms of k: P=k/4,Q=k/7,R=k/2. Thus P:Q:R=1/4:1/7:1/2.
P:Q:R=14:8:28⟹7:4:14
Calculate Total Parts
Sum the parts of the ratio to find the denominator for the share calculation.
7+4+14=25
Determine R's Share
R's share corresponds to 14 parts out of 25. Multiply this fraction by the total amount ₹3300.
R=2514×3300=14×132=1848
D is correct because R's share of the ₹3300 is calculated as ₹1848 based on the ratio 7:4:14.
This concept of equating products to find ratios is frequently used in 'Partnership' and 'Time and Work' problems where efficiencies are given.
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