Question

The ratio of the present age of Giri and hari is 5:8 , 12 years hence, the ratio of their ages will be 11:14. Find the difference in their persent ages?​

Answer 1

${\underline{\frak{\purple{Question:-}}}}$

• To find the difference of ages of Hari and Giri.

${\underline{\frak{\purple{Given:-}}}}$

• Ratio of present ages of Giri and Hari is 5:8

• Ratio of ages after 12 years is 11:14

${\underline{\frak{\purple{Solution:-}}}}$

Let, Present ages be 5x and 8x (5:8)

• Age of Giri be 5x

• Age of Hari be 8x

$\sf \: 5: 8 \: (after \: 12 \: \: years)\longrightarrow \: 11: 14$

$\sf \longmapsto \: 5x + 12 : 8x + 12 = 11 : 14$

$\sf\longmapsto \small\small \frac{5x + 12}{8x + 12} = \frac{11}{14} (\sf \: cross \: multiply) \\ \\ \sf\longmapsto \small 70x + 168 = 88x + 132 \\ \\ \sf\longmapsto \small \: 88x - 70x = 168 - 132 \\ \\ \longmapsto\sf \small 18x = 36 \\ \\ \longmapsto\sf\small \: x = \frac{36}{18} \\ \\ \bf\longmapsto\small \: x = 2$

So, x = 2.

Hence,

The ratio of age of Giri :-

$\sf \: = 5x \\ = \sf \: 5 \times 2 \\ =\sf 10$

The ratio of age of Hari :-

$\sf \: = 8x \\ =\sf 8 \times 2 \\ \sf \: = 16$

ie, The Present ages of Giri and Hari is 10 and 16.

The difference of their ages is 6.

16 - 10 = 6

Thus Solved !!

Answer 2

The difference in present ages of Giri and Hari is 6 years

Given :

• The ratio of the present age of Giri and Hari is 5 : 8

• 12 years hence, the ratio of their ages will be 11 : 14

To find :

The difference in present ages of Giri and Hari

Solution :

Step 1 of 3 :

Form the equation to calculate present ages of Giri and Hari

Here it is given ratio of the present age of Giri and Hari is 5 : 8

Let present ages of Giri and Hari are 5x years and 8x years respectively

12 years hence ages of Giri and Hari will be (5x + 12) years and (8x + 12) years respectively

So by the given condition

$\displaystyle \sf (5x + 12) : (8x + 12) = 11 : 14$

Step 2 of 3 :

Calculate present ages of Giri and Hari

$\displaystyle \sf (5x + 12) : (8x + 12) = 11 : 14$

$\displaystyle \sf{ \implies } \frac{5x + 12}{8x + 12} = \frac{11}{14}$

$\displaystyle \sf{ \implies } 11(8x + 12) = 14(5x + 12)$

$\displaystyle \sf{ \implies }88x + 132 = 70x + 168$

$\displaystyle \sf{ \implies }18x = 36$

$\displaystyle \sf{ \implies }x = 2$

Giri's present age

= 5x years

= (5 × 2) years

= 10 years

Hari's present age

= 8x years

= (8 × 2) years

= 16 years

Step 3 of 3 :

Calculate difference in present ages of Giri and Hari

Giri's present age = 10 years

Hari's present age = 16 years

Hence difference in present ages of Giri and Hari

= 16 years - 10 years

= 6 years

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