Question

22. Reena is 20 years younger to her
mother after 10 years, her mother will
be twice as old as Reena will be then.
How old is Reena now? *
5 years
10 years
12 years
14 years​

Answer 1

Step-by-step explanation:

Therefore reena will be 10 years old .

Answer 2

SOLUTION -:

Lets Reena 's present age be x year

hence , her mother present age = ( x + 20 ) years

[ As Reena is 20 years younger, her

mother's age is 20 year more than her age ]

After 10 years ,

Reena's age will be = ( x + 10 ) years

and her mother age will be [( x +20 )+ 10 ] years

According to this problem,

Reena's mother will be 2 time as old as Reena after 10 years

because:-

$( \: x + 20) + 10 = 2(x + 10) \\ x + 20 + 10 = 2x + 20 \\ x + 30 \: = 2x + 20 \\ 2x + 20 = x + 30 \: \: \\ transposing \: \: lhs \: to \: rhs \:$

$2x = x + 30 - 20 \\ transpose \: 20 \: to \: rhs \: \\ 2x = x + 10 \\ 2x - x = 10 \\ x = 10$

because,

Renna present age is 10 year .

Check : Reena's present age= 10 years

Reena's mother's age= 30 year

After 10 year's, Reena's age = 10 + 10 = 20 year's

After 10 year's, Mother' s age 30 + 10 = 40 years and 40 is twice of 20

Thus , the answer of Reena present age = 10 years