Question

father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?

40 years
32 years
33 years
45 years
22 years

Answer 1

Answer:

45 years

Step-by-step explanation:

Father’s Age: 2x

Daughter’s Age: x

(2x-20) = 10(x-20)

2x-20 = 10x - 200

180 = 8x

Solving,

x = 22.5

therefore, father’s age is 45 years.

Answer 2

Given : Father is twice as old as his daughter. 20 years ago, the age of the father was 10 times the age of the daughter.

To Find : The present age of the father?

ㅤㅤ━━━━━━━━━━━━━━

❍ Let us assume that, the present age of his daughter is 'x' and father is '2x'. 20 years ago,

↠ Age of his daughter = x - 20

↠ Age of the father = 2x - 20

$\boldsymbol{\underline{According \: to \: the \: question,}}$

$\sf{ \Longrightarrow \: 2x - 20 = 10(x - 20) }$

$\sf{ \Longrightarrow \: 2x - 20 = 10x - 200}$

$\sf{ \Longrightarrow \: (-20) + 200 = 10x - 2x}$

$\sf{ \Longrightarrow \: 180 = 8x}$

$\sf{ \Longrightarrow \: x = \cancel\dfrac{180}{8} }$

$\red{\sf{ \Longrightarrow \: x = 22.5}}$

Hence,

➲ Present age of father = 2 × 22.5 = 45 years

ㅤ

So, option (D) 45 years is correct. ✓

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬