Question

Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years
hence, the ratio of their ages will become 11:9 respectively. What is Anand's
present age in years?

a)24
b)27
C) 40
d) 43​

Answer 1

Answer :-

• Option a is correct.

• Anand's present age is 24 years.

Given :-

• Present ages of Sameer and Anand are in the ratio 5 : 4.

• Three years hence, the ratio of their ages will become 11 : 9.

To find :-

• Their present ages.

Step-by-step explanation :-

• The present ages of Sameer and Anand are in the ratio 5 : 4, so let their present ages be 5x and 4x respectively.

Three years later,

• Sameer's age will be 5x + 3.
• Anand's age will be 4x + 3.

It has been given that :-

• After 3 years, their ages will be in the ratio 11 : 9.

-------------------------

Hence,

$\sf \dfrac{5x + 3}{4x + 3} = \dfrac{11}{9}$

By cross multiplication,

$\rm9 \: (5x + 3) = 11 \: (4x + 3)$

Removing the brackets by multiplying the numbers outside the brackets with the numbers inside the brackets,

$\rm45x + 27 = 44x + 33$

Putting the constant and variable terms on different sides by the method of transposition,

$\rm45x - 44x = 33 - 27$

On simplifying,

$\overline{ \boxed{ \rm x = 6}}$

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Therefore,

$\bf Anand's \: age = 4x = 4 \times 6 = 24.$