Question

Four years ago, the average ages of 5 persons A, B, C, D and E is a prime number. If A’s age is 50% of the age of C and after 12 years the ratio of the ages of B to D is 3:2, then find the present age of E.​

Answer 1

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Answer 2

Given : Four years ago, the average ages of 5 persons A, B, C, D and E is a prime number. If A’s age is 50% of the age of C and after 12 years the ratio of the ages of B to D is 3:2.

To find : let present age of A = x, 4 years ago, A = x - 4

present age of B = y , 4 years ago, B = y - 4

present age of C = z, 4 years ago, C = z - 4

present age of D = w, 4 years ago, D = w - 4

present age of E = r , 4 years ago, E = r - 4

now average ages = (A + B + C + D + E)/5

⇒n = (x + y + z + w + r - 20)/5 = (x + y + z + w + r)/5 - 4

⇒(x + y + z + w + r) = 5(n + 4).....(1)

A's age is 50% of age of C

i.e., A/C = 1/2

so x/z = 1/2 ⇒z = 2x .........(2)

after 12 years, B/D = 3/2

⇒(y + 12)/(w + 12) = 3/2

⇒2y + 24 = 3w + 36

⇒2y = 3w + 12

⇒y = 1.5w + 6 ........(3)

here there are six variables and we have just three equations so it can't possible to find out the present age of E.

Therefore the present age of E can't be determined.