Question

13. 10 years ago Charu's mother was 4 times as old as her daughter. Ten
years hence the mother will be twice as old as her daughter. What is the
present age of Charu ?
(b) 18
(c) 20
(d) 22
(a) 16​

Answer 1

Answer:

(c) 20

Step-by-step explanation:

Let Charu present age be 'x'

Mother age 10 years ago = 4(x-10)

10 years hence

Mother age = 2(x+10)

Equating ,

4x-40+20=2x-20

= 4x-2x -20=20

= 2x =40

=x = 20

Hence , Charu present age is 20 years.

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Answer 2

Let present age of Charu be "M" years and present age of her mother be "N" years.

Ten years ago, Charu's mother was four times as old aa her daughter.

According to question,

=> (N - 10) = 4(M - 10)

=> N - 10 = 4M - 40

=> N = - 40 + 10 + 4M

=> N = 4M - 30 ____ (eq 1)

Ten years, hence mother will be twice as old her daughter.

According to question,

=> (N + 10) = 2(M + 10)

=> 4M - 30 + 10 = 2M + 20 [From (eq 1)]

=> 4M - 20 = 2M + 20

=> 4M - 2M = 20 + 20

=> 2M = 40

=> M = 20

(Age of Charu = 20 years)

Put value of M in (eq 1)

=> N = 4(20) - 30

=> N = 80 - 30

=> N = 50

(Age of Charus mother = 50 years)

∴ Present age of Charu is 20 years.

Answer :

Option c) 20