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Among five people named A, B, C, D and E, each has a certain age. C is thrice the age of D. The age of A is 6. D is half the age of E. B is twice the age of A. If E is four times the age of B, what is the age of C?
70
75
76
72
72
Represent each person's age as a variable based on D. Connect the relations until you isolate D, then solve for C.
Represent each person's age as a variable based on D. Connect the relations until you isolate D, then solve for C.
Establish known variables
A = 6. B = 2 * A = 12. E = 4 * B = 48.
Calculate D
Given D = E / 2, substitute E = 48: D = 48 / 2 = 24.
Calculate C
Given C = 3 * D, substitute D = 24: C = 3 * 24 = 72.
A: 70 is incorrect as it does not satisfy the relationship between C and D; B: 75 is incorrect as it is not a multiple of 3 (the ratio C:D=3:1); C: 76 is incorrect as it results from miscalculating the multiplier steps.
D is correct because following the chain A(6) тЖТ B(12) тЖТ E(48) тЖТ D(24) leads to C = 3 * 24 = 72.
In age puzzles, always express all variables in terms of one base variable (in this case, D or A) to quickly resolve linear equations.
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