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The ages of A and B are in the ratio 5:7. If the difference between their ages is 12 years, what is the age of B?
30 years
42 years
35 years
48 years
42 years
Since the age of B must be a multiple of its ratio part (7), only options that are multiples of 7 are valid. Here, 42 is the only multiple of 7 among the choices.
Ratio of ages of A and B = 5:7, Difference between their ages = 12 years.
Age of B=(Difference of ratio partsRatio part of B)×Actual Difference
Since the age of B must be a multiple of its ratio part (7), only options that are multiples of 7 are valid. Here, 42 is the only multiple of 7 among the choices.
Students often calculate the sum of ages instead of the difference, or assign the age to the wrong person in the ratio by ignoring the sequence A:B.
Define the common multiplier
Let the ages of A and B be 5x and 7x respectively.
A=5x,B=7x
Set up the equation based on difference
Given that the difference between their ages is 12, we can write the equation as 7x−5x=12.
7x−5x=12⟹2x=12
Solve for x
Divide 12 by 2 to find the value of the constant multiplier x.
x=212=6
Calculate the age of B
Substitute x=6 into the expression for B's age, which is 7x.
Age of B=7×6=42
B is correct because the calculated age of B using the ratio constant is 42 years.
This ratio technique is highly effective for solving problems related to mixtures, age, and profit-sharing in quantitative aptitude sections.