Question

{8} The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

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Answer 1

To Find :

• The present ages of Hari and Harry .

Given :

• Ratio of present ages (hari to Harry) = 5:7
• Ratio of their ages after 5 years = 3:4

let's Assume :

Let's Assume that,

Age of Hari = 5x

Age of Harry = 7x

Age of Harry after four years = 7x+4

Age if Hari After four years = 5x+4

Process:

• We will first Assume the ages of Harry and Hari
• Then we will find the ages of them after 4 years
• Then we will compare this to given Ratio
• We will get the value of variable
• We can find present Age.

Solution :

Given, Ratio of ages after 4 years = 3:4

Age of Hari after 4 year = 5x+4

Age of Harry after 4 years = 7x+4

$\large \tt{ \implies \frac{5x + 4}{7x + 4} = \frac{3}{4} }$

$\large{ \tt{ \implies (3)7x + 4 = (4)5x + 4}}$

$\large \tt{ \implies 21x + 12 = 20x + 16}$

$\large{ \tt{ \implies 21x - 20x = 16 - 12}}$

$\large{ \red{ \underline{ \boxed{ \tt{ \bigstar \: x = 4}}}}}$

Hence, x = 4

Hence, ages of :

• Hari = 5x = 5×4 = 20 years
• Harry = 7x = 7×4 = 28 years.

__________________________

Verification :

Let's Verify our answer if we have got correct answer or not.

So, to verify first we will find their ages after four year and compare it with Ratio.

So, Age of Hari after 4 years = 20+4 = 24 years

Age of HARRY after 4 years = 28+4 = 32 years .

So, Ratio of ages

= 24:32

= (8×3):(8×4)

After cancelling 8, we get,

24:32

= 3:4

This Ratio is Same as in the question, hence our answer is correct.

Hence Verified !

Answer 2

☆ Given :-

• The ages of Hari and Harry are in ratio 5 : 7
• After 4 years the ratio of their ages will be 3 :4

☆ To Find :-

• Present ages of Hari and Harry

☆ Assumption :-

• Let the age of Hari be 5x
• Let the age of Harry be 7x

☆ Solution :-

Now, According to the question,

• Their ages after 4 years will be 5x + 4 and 7x + 4 respectively

Now,

$: \sf \implies \: \frac{5x + 4}{7x + 4} = \frac{3}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ : \sf \implies \:4(5x + 4) = 3(7x + 4) \\ : \sf \implies \:20x + 16 = 21x + 12 \: \: \: \\ : \sf \implies \:21x - 20x = 16 - 12 \: \: \: \\ : \sf \implies \:x = 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bigstar \: \boxed { \large\tt \red{ \therefore \: age \: of \: hari = 5 x = 5 \times 4 = 20 }}$

$\bigstar \: \boxed { \large\tt \orange{ \therefore \: age \: of \: harry = 7 x = 7 \times 4 = 28 }}$