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. cannot be determind c. 40 d. none e. 27

Answer 1

Present age

Ratio = Sameer : Anand = 5 : 4 (Given)

Let x be the constant ratio:

Ratio = Sameer : Anand = 5x : 4x

3 years later:

Sameer = 5x + 3

Anand = 4x + 3

3 years later:

Ratio = Sameer : Anand = 11 : 9 (Given)

let y be the constant ratio:

Ratio = Sameer : Anand = 11y : 9y

Form equations:

5x + 3 = 11y ----------------  [ 1 ]

4x + 3 = 9y ----------------  [ 2 ]

[ 1 ] x 4 : 20x + 12 = 44y   ----------------  [ 3 ]

[ 2 ] x 5 : 20x + 15 = 45y ----------------  [ 4 ]

[ 4 ] - [ 3 ]: y = 3  ----------------  Sub into  [ 1 ]  

5x + 3 = 11 (3)

5x + 3 = 33

5x = 30

x = 6

Find Ananda's age:

Ananda = 4x = 4(6) = 24 years old

Answer: (a) 24 years old

Answer 2

Answer:

Let the present age of Sameer be 5x and Anand be 4x respectively.

$\rule{130}2$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{Sameer+3}{Anand+3}=\dfrac{11}{9}\\\\\\:\implies\sf \dfrac{5x + 3}{4x + 3} = \dfrac{11}{9} \\\\\\:\implies\sf (5x + 3) \times 9= 11 \times (4x + 3)\\\\\\:\implies\sf 45x + 27 = 44x + 33\\\\\\:\implies\sf 45x - 44x = 33 - 27\\\\\\:\implies\:\underline{\boxed{\red{\bf x = 6\:years}}}\: \orange\bigstar$

$\rule{130}2$

☯ $\underline{\boldsymbol{Present\: Age\:of\: Sameer\:\&\: Anand:}}$

$\bullet\:\:\textsf{Sameer = 5x = 5(6) = \textbf{30 years}}\\\bullet\:\:\textsf{Anand = 4x = 4(6) = \textbf{24 years}}$

$\rule{130}2$