Question

Mrs.Jain is 27 years older than her daughter Nilu. After 8 years she will be twice as old as Nilu.Find thier present ages.​

Answer 1

Given :

Mrs.Jain is 27 years older than her daughter Nilu. After 8 years she will be twice as old as Nilu. Find thier present ages.

To Find :

• The present age of Mrs. Jain and Nilu

Solution :

Let us assume :

Nilu's age be x

Then Mrs. Jain is 27 yrs older than Nilu = x + 27

After 8 years :

Nilu's age = x + 8

Mrs. Jain's age = x + 27 + 8 → x + 35

Ratio of ages after 8 years :

Mrs. Jain = 2

Nilu = 1

Henceforth, the equation is :

$\sf\mapsto \frac{x + 35}{x + 8} = \frac{2}{1}$

By cross multiplying we get :

$\mapsto \sf 1(x + 35) = 2(x + 8)$

$\mapsto \sf x + 35 = 2x + 16$

$\mapsto \sf 2x - x = 35 - 16$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \green{ \underline{ \pink{\boxed{ \blue{\sf x = 19}}}}}$

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Now, to find their present ages :

Nilu's present age = x = 19 years

Mrs. Jain's present age = x + 27 = 19 + 27 = 46 years

Hence, Mrs. Jain is 46 years and Nilu is 19 years