Question

Arun's age is four years more than prasant's age . 4 years ago, the ratio of their ages was 5:4 .Find their present ages

Answer 1

Solution

Let,

• Prasant's present age be (a) yrs
• Arun's present age be (a+4) yrs

4 yrs ago,

• Age of Prasant was (a-4) yrs
• Age of Arun was (a+4-4=a) yrs

A.T.Q

$\sf \large{\frac{a}{(a - 4)}=\frac{5}{4}}$

$\sf \leadsto{4a = 5(a - 4)}$

$\sf \leadsto{4a = 5a - 20}$

$\sf \leadsto{4a - 5a = - 20}$

$\sf \leadsto{ \cancel{-}a = \cancel{-}20}$

$\sf\large\leadsto{a = 20}$

Verification

$\sf{LHS = \frac{20}{20 - 4} = \frac{20}{16} = \frac{5}{4}}$

$\sf{RHS = \frac{5}{4}}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\frac{5}{4}=\frac{5}{4}}$

$\sf\large \: \: \: \: \: \: \: \: \:{LHS = RHS}$

Hence,verified!!

Therefore

• Prasant's present age = a = 20
• Arun's present age = (a+4) = (20+4) = 24

Hence,their present ages are 20 and 24 respectively.

Answer 2

Answer:—

Let,

The age of Prashant be x. This implies Arun's age is x + 4.

Before 4 years their ages would have been:

• Prashant = x - 4,
• Arun = x

That was in the ratio 4 : 5

=> x - 4 : x = 4 : 5

Product of Means = Product of Extremes

=> ( x - 5 ) ( 4 ) = ( 5 ) ( x )

=> 5x - 20 = 4x

=> 5x - 4x = 20

=> x = 20 years

Hence,

Age of Prashant is 20 years.

Age of Arun is 20 + 4 = 24 years

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