Question

The sum of the age of mother and a mother
and her daughter is 60 years. 12 years ago
the mother was eight times as old as her
daughter. How old is the daughter at present?
(a) 20 yr (b) 28 yr
(c) 16 yr (d) 12 yr​

Answer 1

Answer :-

Present age of daughter = 16 years.

Option (c) 16 years

$\rule{150}2$

Let the -

• the present age of mother be M years
• present age of daughter be D years

The sum of ages of mother and her daughter is 60 years.

=> $\sf{M\:+\:D\:=\:60}$

=> $\sf{M\:=\:60\:-\:D}$ ....(1)

12 years ago, the mother was eight times as old as her daughter.

12 years ago -

• Age of mother = (M - 12) years
• Age of daughter = (D - 12) years

According to question,

=> $\sf{M\:-\:12\:=\:8(D\:-\:12)}$

=> $\sf{M\:-\:12\:=\:8D\:-\:96}$

=> $\sf{60\:-\:D\:-\:12\:=\:8D\:-\:96}$ [From (1)]

=> $\sf{48\:-\:D\:=\:8D\:-\:96}$

=> $\sf{48\:+\:96\:=\:8D\:+\:D}$

=> $\sf{144\:=\:9D}$

=> $\sf{\frac{144}{9}\:=\:D}$

=> $\sf{16\:=\:D}$

=> $\boxed{\sf{D\:=\:16}}$

$\therefore$ Present age of daughter is 16 years

Substitute value of D = 16 in (1)

=> $\sf{M\:=\:60\:-16}$

=> $\boxed{\sf{M\:=\:44}}$

$\therefore$ Present age of mother is 44 years

____________________

Verification :-

From above calculation, we have -

• present age of mother = M = 44 years
• present age of daughter = D = 16 years

Substitute value of M & D in (1)

→ 44 = 60 - 16

→ 44 = 44

Answer 2

Answer:

0ption c is correct

Let the present age of mother be x

Then, the present age of daughter be (60-x)years.

12 years ago,

The age of mother =(x-12)years

The age of daughter= [(60-x)-12]years

=[60-x-12]years

= (48-x)years

Atq,

x-12 = 8 (48-x)

=> x-12 = 384-8x

=> x+8x = 384+12

=>9x = 396

=>x = 396/9

=> x = 44

Hence, the present age of mother = 44 years.

present age of daughter =(60-44)years

= 16 years