Question

The difference in ages between a boy and his younger brother is 6 years.The younger brother is 6 years older than his sister. The sum of ages of the younger brother and his sister is 30.How old are the three children?​

Answer 1

Answer:

The ages of 3 children are 24, 18 and 12.

Step-by-step explanation:

Let x, y and z be the ages of the bot, younger brother and sister.

difference in ages between a boy and his younger brother is 6 years

=> x - y = 6  ----------> equation 1

younger brother is 6 years older than his sister

=> y = z + 6 => y - z = 6 ----------> equation 2

sum of ages of the younger brother and his sister is 30

=> y + z = 30 ----------> equation 3

Add equation 2 and 3

y - z = 6

y + z = 30

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2y = 36 => y = 18, z = 12.

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Substitute value of y in equation 1

x = y + 6 = 18 + 6 = 24.