Question

The ages of Arun and Rahul are in the ratio 7: 5. Ten years
hence, the ration of their ages will be 9: 7, find their present ages


Give STEP BY STEP EXPLANATION too, or I won't mark you as brainliest.

Answer 1

Step-by-step explanation:

let

Arun = 7x

Rahul = 5x

.

.

.

.

After 10 years

Arun will be = 7x + 10

Rahul will be = 5x + 10

.

.

.

.

But, ATQ

Arun =

$\frac{7x + 10}{5x + 10} = \frac{9}{7}$

7 ( 7x + 10 ) = 9 ( 5x + 10 ). { cross multiplication}

.

.

.

.

49x + 70 = 45x + 90

49x - 45x = 90 - 70

4x = 20

x =

$\frac{20}{4} = 5$

.

.

.

.

Arun = 7x = 7 x 5 = 35 yrs

Rahul = 5x = 5 x 5 = 25 years

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Ages of Arun and Rahul are in the ratio 7: 5

$\:\:$

• Ten years hence, the ratio of their ages will be 9: 7

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Their present ages

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the present ages of Arun and Rahul be 7x & 5x respectively

$\:\:$

$\underline{\bold{\texttt{Arun's present age :}}}$

$\:\:$

➠ 7x ------- (1)

$\:\:$

$\underline{\bold{\texttt{Rahul's present age :}}}$

$\:\:$

➠ 5x ------- (2)

$\:\:$

$\underline{\bold{\texttt{Arun's age after 10 years :}}}$

$\:\:$

➠ 7x + 10

$\:\:$

$\underline{\bold{\texttt{Rahul's age after 10 years :}}}$

$\:\:$

➠ 5x + 10

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

Ten years later , the ratio of their ages will be 9: 7

$\:\:$

Thus,

$\:\:$

➜ $\sf \dfrac { 7x + 10 } { 5x + 10 } = \dfrac { 9 } { 7 }$

$\:\:$

➜ 45x + 90 = 49x + 70

$\:\:$

➜ 49x - 45x = 90 - 70

$\:\:$

➜ 4x = 20

$\:\:$

➜ $\sf x = \dfrac { 20 } { 4 }$

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➨ x = 5 ----- (3)

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⟮ Putting x = 5 from (3) to (1) ⟯

$\:\:$

➜ 7x

$\:\:$

➜ 7(5)

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➨ 35

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• Hence present age of Arun is 35 years

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⟮ Putting x = 5 from (3) to (2) ⟯

$\:\:$

➜ 5x

$\:\:$

➜ 5(5)

$\:\:$

➨ 25

$\:\:$

• Hence present age of Rahul is 25 years

$\:\:$

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