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?

Answer 1

Let the ages of Sameer and Anand be x and y respectively,

Then According to Question,

x/y = 5/4  ⇒ 4 x = 5 y 

4 x - 5 y = 0                               ...............(1)

Also, x+3/y+3 = 11/9

9(x+3) = 11(y+3)

9 x + 27 = 11 y + 33

9 x - 11 y = 6                             ...............(2)
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From (1) and (2) Subtracting them,

(1) × 9 ⇒ 36 x - 45 y = 0

(2) × 4 ⇒ 36 x - 44 y = 24
                (-)      (+)       (-)
                _____________

                          - y  = - 24
                _____________

Then y = 24 yrs and so, x = 30 yrs.
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Hence ages of Sameer = 30 yrs and ages of Anand = 24 yrs.
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  ☺☺☺ Hope this Helps ☺☺☺

Answer 2

Answer:

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

$\rule{130}2$

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

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

$\rule{130}2$

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

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

$\rule{130}2$