Question

5. Pushpa is twice as old as Rita was
two years ago. If the difference
between their ages be 2 years, how
old is Pushpa today?
(A) 6 years
(B) 8 years
(C) 10 years
(D) 12 years
​

Answer 1

✬ Pushpa = 8 years ✬

Step-by-step explanation:

Given:

• Pushpa is twice of Rita's two years ago age.
• Difference between their ages is 2 years.

To Find:

• What is present age of Pushpa ?

Solution: Let Pushpa's age be x years and Rita's age be y years. Therefore,

➟ Rita's age 2 years ago = (y – 2) years

∴ Pushpa's age = 2 times of Rita's age

➟ Pushpa's age = 2(y – 2) years

➟ x = 2(y – 2) ......(1)

A/q

• Difference between their ages is 2 years.

∴ Pushpa age – Rita age = 2 years

➮ x – y = 2

➮ x = 2 + y.....(2)

[ Now put the value of x in equation (1) from (2) ]

$\implies{\rm }$ x = 2(y – 2)

$\implies{\rm }$ 2 + y = 2y – 4

$\implies{\rm }$ 2 + 4 = 2y – y

$\implies{\rm }$ 6 = y

So, age of

➯ Rita is y = 2 years

➯ Pushpa is x = 2 + 6 = 8 years

Hence, Pushpa is 8 years old today. (Option B is correct).

Answer 2

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Pushpa is 8 years old today.