Question

the ratio of present ages of albert and salim is 8:7 4years ago ratio of there ages will be 6:5 find the present ages​

Answer 1

Given:

• Ratio of present ages of albert and salim is 8:7
• 4 years ago ratio of there ages were 6:5

To Find:

• Their present ages

Solution:

Let present age of Albert be = 8x

And present age of Salim be = 7x

Now

According to question:

4 years ago ratio of there ages were 6:5

Albert's age = 8x - 4

Salim's age = 7x -4

$\leadsto$ 8x - 4/ 7x - 4 = 6/5

$\leadsto$ 5( 8x - 4 ) = 6( 7x - 4 )

$\leadsto$ 40x - 20 = 42x - 24

$\leadsto$ 2x = 4

$\leadsto$ x = 2

Now

Present age of Albert = 8x = 8(2) = 16 years

Present age of Salim = 7x = 7(2) = 14 years

Hence, present ages of Albert and Salim are 16 and 14 years.

Answer 2

Given :-

Ratio of present ages of albert and Salim = 8:7

Before 4 years the ratio were 6:5

To Find :-

Present ages

Concept

$\leadsto$At first we need to assume their ages a variable y.

$\leadsto$ Then the ratio will become 8y and 7y

$\leadsto$ Then, we will cross multiply it

Solution :-

Let their ages be 8y and 7y

So,

Present age

$\sf\dfrac{8y}{7y}$

Before 4 years

$\bf \dfrac{8y - 4}{7y - 4} = \dfrac{6}{5}$

Now,

We have to cross multiply them

$\sf 5\bigg(8y - 4\bigg)=6\bigg(7y - 4\bigg)$

$\sf (5 \times 8y) - (5 \times4) = (6 \times 7y) - (6 \times 4)$

$\sf 40y - 20 = 42y - 24$

$\sf 42y - 40y =2 4 -20$

$\sf 2y =2 4 - 20$

$\sf 2y = 4$

$\sf y = \dfrac{4}{2}$

y = 2

Age of Albert

8y

8(2)

16 years

Age of Salim

7y

7(2)

14 years