Question

In a colony average age of boys is 14 and the average age of girls is 17 years.if the average age of children in the colony is 15 years,find the ratio of boys to that of girls.
(A)1:2
(B)2:1
(C)2:3
(D)3:2

Answer 1

Answer:

2:1

Step-by-step explanation:

Here we can use alligation

i.e

14. 17

15

2. : 1

subtract diagonally

Answer 2

Answer:

Required ratio of boys to that of girls is 2:1.

So, option b is the correct answer.

Step-by-step explanation:

Given,

average age of boys = 14 years

average age of girls = 17 years

and average age of all children = 15 years

Let number of boys be x and number of girls be y.

So,

Sum of number of boys

$= 14 \times number \: of \: boys \\ = 14 \times x \\ = 14x$

Sum of number of girls

$= 17 \times number \: of \: girls \\ = 17 \times x \\ = 17x$

Sum of total number of children

$= 15 \times sum \: of \: total \: number \: of \: children \\ = 15 \times (x + y) \\ = 15x + 15y$

Now according to question,

$14x + 17y = 15x + 15y \\ 14x - 15x = 15y - 17y \\ - x = - 2y \\ x = 2y \\ \frac{x}{y} = \frac{2}{1} \\ x:y = 2:1$

Required ratio of boys to that of girls is 2:1.

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