Question

Q-20. The ages of Kartik and Madan are in the ratio 3:5. Two years later
the sum of their ages will be 36 years. What are their present ages?
O A. 12 & 20
B. 20 & 12
O C.22 & 20
O D. 12 & 28​

Answer 1

EXPLANATION.

Let the age of kartik be = x

Let the age of madan be = y

To find the present age.

According to the question,

The ages of kartik and madan are in the

ratio = 3:5

=> x/y = 3/5

=> 5x = 3y

=> 5x - 3y = 0 ......(1)

Two years later, the sum of their ages will

be = 36 years.

=> Age of kartik = ( x + 2 ) years.

=> Age of madan = ( y + 2 ) years.

=> ( x + 2 ) + ( y + 2 ) = 36

=> x + y = 36 - 4

=> x + y = 32 ........(2)

From equation (1) and (2) we get,

=> 5x - 3y = 0 .....(1)

=> x + y = 32 .....(2)

=> multiply equation (1) by 1

=> multiply equation (2) by 3

we get,

=> 5x - 3y = 0

=> 3x - 3y = 96

=> 8x = 96

=> x = 12

put the value of x = 12 in equation (2)

we get,

=> 12 + y = 32

=> y = 32 - 12

=> y = 20

Therefore,

present age of kartik = x = 12 years.

present age of madan = y = 20 years.

Answer 2

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Given:}}}$

• We have been given that Kartik and Madan age are in ratio 3:5
• Two years later, sum of their ages will be 36

$\large\underline{\sf{\blue{To \: Find:}}}$

• We have to find the present ages of Kartik and Madan

$\large\underline{\sf{\blue{Solution:}}}$

Given, The ages of Kartik and Madan are in the ratio 3:5. Let us assume

$\boxed{\sf{Present \: age \: of \: Kartik = 3x}}$

$\boxed{\sf{Present \: age \: of \: Madan = 5x}}$

$\sf{}$

$\large\underline{\mathfrak{\red{According \: to \: the \: Question:}}}$

Two years Later the sum of their ages will be 36

Kartik age = 3x + 2

Madan age = 5x + 2

$\implies \boxed{\sf{Sum \: of \: Ages = 36}}$

$\implies \sf{3x + 2 + 5x + 2 = 36}$

$\implies \sf{8x + 4= 36}$

$\implies \sf{8x = 32}$

$\implies \sf{x = \dfrac{32}{8}}$

$\implies \boxed{\sf{x = 4}}$

$\sf{}$

Present age of kartik (3x) = 12 years

Present age of Madan (5x) = 20 years

Hence Option A is correct

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$\large\purple{\underline{\underline{\mathtt{Extra \: Information:}}}}$

• Tips for solving ages Question
• If the current age is x, then n times the age will be nx.
• If the current age is x, then age n years later will be x + n.
• If the current age is x, then age n years ago was x - n.
• The ages are in a ratio a : b then ages will be ax and bx.
• If the current age is x, then 1/n of the age will be x/n

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