Question

18) A's present age in years is 20% of B's age. After
30 years, A's age will be 1/2 of B's. The sum of the present
ages of A and B is
A) 40 years
B) 60 years
C) 80 years
D) 100 years
5​

Answer 1

Answer:

(B) 60

Step-by-step explanation:

Given,

A's present age in years is 20% of B's age.

A=20%of B

A/B=20/100

Let A/B=1x/5x

After  30 years

A=1x+30

B=5x+30

A's age will be 1/2 of B's

1x+30=1/2(5x+30)

2x+60=5x+30

3x=30

x=10

Present ages's

A=10

B=5*10

 =50

A+B=60

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

A's present age in years is 20% of B's age. After 30 years, A's age will be 1/2 of B's. The sum of the present ages of A and B is

A) 40 years

B) 60 years

C) 80 years

D) 100 years

EVALUATION

Here it is given that A's present age in years is 20% of B's age

Let present age of B is 100x

Then present age of A is 20x

Now after 30 years the ages of A and B will be 20x + 30 years and 100x + 30 respectively

So by the given condition

$\displaystyle \sf{20x + 30 = \frac{100x + 30}{2} }$

$\displaystyle \sf{ \implies \: 40x + 60 = 100x + 30 }$

$\displaystyle \sf{ \implies \:60x = 30 }$

Now the sum of the present ages of A and B

= 20x + 100x

= 120x

= 2 × 60x

= 2 × 30 years

= 60 years

FINAL ANSWER

Hence the correct option is

B) 60 years

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