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₹5400 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.
₹1235
₹947
₹1245
₹1080
₹1080
Convert the coefficients (6, 3, 8) into ratios by taking their LCM (24). Then, divide the LCM by each coefficient to get P:Q:R = 4:8:3. R's share is 153×5400.
Total amount = ₹5400. Relationship given: 6P = 3Q = 8R.
P=61k,Q=31k,R=81k
Convert the coefficients (6, 3, 8) into ratios by taking their LCM (24). Then, divide the LCM by each coefficient to get P:Q:R = 4:8:3. R's share is 153×5400.
Many students mistakenly assume the ratio of P, Q, and R is 6:3:8. In equations like aP = bQ = cR, the ratio is a1:b1:c1.
Establish the relationship
Set the given equality to a constant k: 6P=3Q=8R=k. This implies P=k/6, Q=k/3, and R=k/8.
P:Q:R=61:31:81
Convert to whole number ratio
Find the LCM of the denominators (6, 3, 8), which is 24. Multiply each term by 24 to simplify the ratio.
P:Q:R=4:8:3
Calculate R's share
Total ratio parts = 4+8+3=15. R's share is 153 of the total amount ₹5400.
R=153×5400=3×360=1080
D is correct because R's share is calculated as 153×5400=₹1080.
This inverse ratio logic is frequently tested in 'Work and Wages' problems where efficiency is inversely proportional to time.
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