Question

In a family there are five children namely A, B, C, D and E. Each of them was born at the interval of 5 years. Now the sum of their ages is 75. Find the age of the youngest child.

Answer 1

Answer:

Let

Age of A = a

Age of B = a + 5

Age of C = a + 5 + 5 = a + 10

Age of D = a + 5 + 5 + 5 = a + 15

Age of E = a + 5 + 5 + 5 + 5 = a + 20

a + a + 5 + a + 10 + a + 15 + a + 20 = 75

Grouping like terms

(a + a + a + a + a) + (5 + 10 + 15 + 20) = 75

5a + 50 = 75

5a = 75 - 50

5a = 25

a = 25/5

a = 5

Age of youngest child = 5 years

Answer 2

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Since, the children were born at the interval of three years ,let us assume their age as x, x+3,x+6,x+9,x+12.

given- the sum of five children is 50

therefore,

x+x+3+x+6+x+9+x+12 = 50

5x+30 = 50

5x = 50-30

5x=20

x=4

Hence, age of the youngest child is 4 years.