Question

in
The present age of two brother are
the ratio 3:4 tive years back their
ages were in the ratio of 5:7 Find
their present age​

Answer 1

Answer:

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Answer 2

$\large\boxed{\fcolorbox{black}{yellow} {Answer}}$

The present age of younger brother is 30 years.

The present age of older brother is 40 years.

$\large\boxed{\fcolorbox{blue}{yellow} {Step - by - step explanation }}$

Given

1) The present age of two brothers is in the ratio =>

3:4.

2) Five years ago their ages in the ratio => 5:7.

To find

The present ages of the two brothers.

Solution

Suppose the present age of younger brother = x years

And the present age of older brother = y years

From the first condition,

x : y = 3 : 4

$\frac{x}{y} = \frac{3}{4} \\ \\ 4x = 3y \\ 4x - 3y = 0 \: \: \: ......(1)$

From the second condition,

Five years ago age of younger brother = (x - 5) years

Five years ago age of older brother = (y - 5) years

(x - 5) : (y - 5) = 5 : 7

$\frac{(x - 5)}{(y - 5)} = \frac{5}{7} \\ \\ 7(x - 5) = 5(y - 5) \\ 7x - 35 = 5y - 25 \\ 7x - 5y = - 25 + 35 \\ 7x - 5y = 10 \: \: \: ......(2)$

Multiplying equation (1) by 5 and equation (2) by 3 we get,

$4x - 3y = 0 \: \: \: ....(1)\\ 5(4x - 3y) = 5 \times 0 \\ 20x - 15y = 0 \: \: \: .....(3) \\ \\ 7x - 5y = 10 \: \: \: \: .....(2) \\ 3(7x - 5y) = 3 \times 10 \\ 21x - 15y = 30 \: \: \: ....(4)$

Subtracting equation (3) from equation (4) we get,

$21x - 15y = 30 \: \: \: \: ....(4) \\ - \: 20x - 15y = 0 \: \: \: ...(3) \\ - - - - - - - - - ---- \\ x = 30$

Putting x = 3 in equation (1) we get,

$4x - 3y = 0 \: \: \: \: ...(1) \\ 4(30) - 3y = 0 \\ 120 - 3y = 0 \\ 120 - 0 = 3y \\ 120 = 3y \\ \\ y = \frac{120}{3} \\ y = 40 \:$

Ans. :

The present age of younger brother is 30 years.

The present age of older brother is 40 years.

Hope it helps!

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