Question

Solved Examples(Set 1) - Age
1. Ten years ago, P was half of Q's age. If
the ratio of their present ages is 3:4,
what will be the total of their present
ages?
A. 30
B. 45
C. 35
D. 40​

Answer 1

Answer:

The total of their present ages = 35 years

Step-by-step explanation:

Given:

• Ten years ago, P was half of Q's age.
• If the ratio of their present ages is 3:4.

To find:

• What will be the total of their present ages?

Solution:

Let the present ages of P and Q be 3x and 4x respectively.

According to the problem,

• ( 3x - 10 ) = ½ ( 4x - 10 )
• 2( 3x - 10 ) = ( 4x - 10 )
• 6x - 20 = 4x - 10
• 6x - 4x = - 10 + 20
• 2x = 10
• x = 10/2
• x = 5

Now, substitute the value of x to find their respective ages, we have:

• P's age = 3 × 5
• P's age = 15 years

• Q's age = 4 × 5
• Q's age = 20 years

• Total of their present ages = P's age + Q's age
• Total of their present ages = 15 + 20
• Total of their present ages = 35 years

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