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An amount is distributed among A, B and C in the ratio of 5:7:15. If B's share is ₹1,400 out of the total amount, then the total amount is:
₹8,100
₹4,200
₹2,700
₹5,400
₹5,400
Find the value of 1 ratio unit by dividing B's share by its ratio (1400/7=200), then multiply by the sum of all parts (5+7+15=27). Calculation: 200×27=5400.
Ratio of A, B, and C = 5 : 7 : 15. B's share = ₹1,400.
Total Amount=(RatioA+RatioB+RatioC)×(RatioBValueB)
Find the value of 1 ratio unit by dividing B's share by its ratio (1400/7=200), then multiply by the sum of all parts (5+7+15=27). Calculation: 200×27=5400.
Commonly students multiply 1400 by the sum of ratios instead of dividing 1400 by 7 first to find the multiplier constant.
Define the ratio parts
The ratio of shares for A, B, and C is given as 5:7:15. Let the multiplier constant be x. Therefore, the shares are 5x, 7x, and 15x respectively.
A=5x,B=7x,C=15x
Find the value of the constant x
Given B's share is ₹1,400. Set the expression for B's share equal to the given value: 7x=1400.
x=71400=200
Calculate the total amount
The total amount is the sum of all parts: Total=5x+7x+15x=27x. Substitute the value of x found in the previous step.
Total=27×200=5400
D is correct because the total amount is ₹5,400, calculated by determining the common ratio unit (₹200) and multiplying it by the sum of all ratio parts (27).
This concept of a common multiplier constant is foundational for Mixture and Alligation problems and Partnership profit-sharing questions.
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