Question

Ratio of present ages of Pankaj and Punit is 5 : 6 and the sum of their ages is 33 years. What will be the difference (in years) of their ages?

A) 2 B) 3 C) 4 D) 5

Answer 1

Answer

The correct answer is B) 3

The difference of Pankaj's age and Punit's age is 3 years

Given

• The ratio of present ages of Pankaj and Punit is 5:6
• The sum of their ages is 33 years

To Find

• The difference of their ages

Solution

Let us consider the age of Pankaj and Punit be x and y years respectively.

According to question

$\sf \implies x : y = 5 : 6 \\\\ \sf \implies \dfrac{x}{y}=\dfrac {5}{6} \\\\ \sf \implies x = \dfrac {5}{6}y\longrightarrow (1)$

Again ,

$\sf \implies x + y = 33 \\\\ \sf \implies \dfrac{5}{6}y + y = 33 \\\\ \sf \implies \dfrac{5y+6y}{6} = 33 \\\\ \sf \implies \dfrac{11y}{6}=33 \\\\ \sf \implies y = \dfrac{33\times6}{11}\\\\ \sf\implies y = 3\times 6 \\\\ \implies\sf y = 18$

Putting the value of y in (1)

$\sf \implies x = \dfrac{5}{6}\times 18 \\\\ \implies \sf x = 5\times 3 \\\\ \sf \implies x = 15$

Thus , the difference of their age is ⇒y - x = 18-15

⇒ y - x = 3

Answer 2

GIVEN

• Ratio of present ages pf Pankaj and Punit is 5:6
• The sum of their ages is 33

SOLUTION

Let the present ages of Pankaj and Punit be x years and y years respectively.

We have the ratio of their age ,

⇒x:y = 5:6

⇒ x/y = 5/6

⇒ x = (5/6)y .........(1)

Again their sum of ages is 33

⇒ x + y = 33

⇒ (5/6)y + y = 33

⇒ (5y + 6y)/6 = 33

⇒ 11y/6 = 33

⇒ y = (33×6)/11

⇒ y = 18

Thus the age of Punit is 18 years

From (1) we have ,

⇒ x = (5×18)/6

⇒ x = 15

And the age of Pankaj is 15 years

Therefore , difference of their ages is 3 years .

Hence , option B) 3 is correct.