Question

The present ages of Esha and Disha are in the ratio 7 : 4. If Esha had been 9 years older and Disha 7 years younger, the age of Esha would have been 3 times the age of Disha. Find their present ages.
please do explain well​

Answer 1

Answer:

esha:3 to disha :1 age ki hogi

Answer 2

$\Large{\mathbb{\underline{GIVEN :}}}$

The present ages of Esha and Disha are in the ratio 7:4. If Esha had been 9 years older and Disha 7 years younger, the age of Esha would have been 3 times the age of Disha.

$\Large{\mathbb{\underline{TO \: FIND :}}}$

What are their present ages?

ㅤㅤ━━━━━━━━━━━━━

$\bullet$ Let us assume, that the present age of Esha and Disha is 7x and 4x respectively.

⭐ After 9 years,

Esha's age = 7x + 9

ㅤ

⭐ Before 7 years,

Disha's age = 4x - 7

According to the question,

ㅤㅤㅤ$\sf{ : \: \implies \: 7x + 9 = 3(4x - 7)}$

ㅤㅤㅤ$\sf{ : \: \implies \: 7x + 9 = 12x - 21)}$

ㅤㅤㅤ$\sf{ : \: \implies \: 7x - 12x = (-21) - 9}$

ㅤㅤㅤ$\sf{ : \: \implies \: (-5x) = -30}$

ㅤㅤㅤ$\sf{ : \: \implies \: x = \dfrac{ \cancel{-30}^{ \: 6} }{ \cancel{-5}_{ \: 1} } }$

ㅤㅤㅤ$\mathfrak{ : \: \implies \: \fbox{x = 6} }$

Therefore, their present ages are :

★ Esha's age★

ㅤㅤㅤㅤ↦ 7x

ㅤㅤㅤㅤ↦ 7 × 6

ㅤㅤㅤㅤ↦ 42

ㅤ

★ Disha's age ★

ㅤㅤㅤㅤ↦ 4x

ㅤㅤㅤㅤ↦ 4 × 6

ㅤㅤㅤㅤ↦ 24

$\small{\mathfrak{\underline{ \therefore \: Their~present~ages~are~42~ \& ~24~ respectively.}}}$