Question

the age of two brothers are in the ratio 8:3.In three years time their ages will be in the ratio 9:4. find the difference between their ages​

Answer 1

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Answer 2

Answer:

Given :-

• The age of two brothers are in the ratio of 8 : 3.
• In three years time there ages will be in the ratio of 9 : 4.

To Find :-

• What is the difference between their ages.

Solution :-

Let,

$\leadsto \bf Age_{(First\: Brother)} =\: 8a\: years$

$\leadsto \bf Age_{(Second\: Brother)} =\: 3a\: years$

✭ After 3 years :-

$\mapsto \sf Age_{(First\: Brother)} =\: (8a + 3)\: years$

$\mapsto \sf Age_{(Second\: Brother)} =\: (3a + 3)\: years$

According to the question,

$\clubsuit$ After 3 years time there ages will be in the ratio of 9 : 4.

$\implies \bf \bigg\{\dfrac{Age_{(First\: Brother)}}{Age_{(Second\: Brother)}}\bigg\} =\: \bigg\{\dfrac{9}{4}\bigg\}$

$\implies \sf \dfrac{(8a + 3)}{(3a + 3)} =\: \dfrac{9}{4}$

By doing cross multiplication we get,

$\implies \sf 4(8a + 3) =\: 9(3a + 3)$

$\implies \sf 32a + 12 =\: 27a + 27$

$\implies \sf 32a - 27a =\: 27 - 12$

$\implies \sf 5a =\: 15$

$\implies \sf a =\: \dfrac{\cancel{15}}{\cancel{5}}$

$\implies \sf a =\: \dfrac{3}{1}$

$\implies \sf\bold{\green{a =\: 3}}$

Hence, the required ages of two brothers are :

☛ Age Of First Brother :-

➵ Age Of 1ˢᵗ Brother = 8a years

➵ Age Of 1ˢᵗ Brother = 8(3) years

➵ Age Of 1ˢᵗ Brother = 8 × 3 years

➵Age Of 1ˢᵗ Brother = 24 years

☛ Age Of Second Brother :-

➵ Age Of 2ⁿᵈ Brother = 3a years

➵ Age Of 2ⁿᵈ Brother = 3(3) years

➵ Age Of 2ⁿᵈ Brother = 3 × 3 years

➵ Age Of 2ⁿᵈ Brother = 9 years

Now, we have to find the difference between their ages :-

➠ Difference between their ages = 24 - 9

➠ Difference between their ages = 15 years

$\therefore$ The difference between their ages is 15 years .

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