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A is twice as old as B. B is 31тАЛ as old as C. The sum of ages of A, B and C is 42 years, find the sum of the ages of A and B.
12 years
21 years
15 years
23 years
21 years
Express all ages in terms of B (the common variable) to get the ratio A:B:C = 2:1:3. The total units 2+1+3 = 6 represent 42, so 1 unit = 7. A+B = 3 units = 3 * 7 = 21.
A is twice as old as B (A = 2B). B is 1/3 as old as C (C = 3B). The sum of ages A + B + C = 42 years.
A+B+C=42
Express all ages in terms of B (the common variable) to get the ratio A:B:C = 2:1:3. The total units 2+1+3 = 6 represent 42, so 1 unit = 7. A+B = 3 units = 3 * 7 = 21.
Students often calculate the value of C or A individually and forget the final requirement to sum only A and B.
Define variables in terms of B
Since A=2B and B=31тАЛC, we can say C=3B.
A=2B,C=3B
Set up the sum equation
Given A+B+C=42, substitute the terms involving B: 2B+B+3B=42.
6B=42
Solve for B
Divide the total sum by 6 to find B's age.
B=642тАЛ=7
Calculate the sum of A and B
Find A=2├Ч7=14. Then, sum of A+B=14+7=21.
A+B=14+7=21
B is correct because the sum of the ages of A and B is 14+7=21 years.
This ratio-based approach is highly applicable to 'Mixture and Alligation' or 'Partnership' problems in competitive exams.
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