Question

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Answer 1

let the common multiple be x

Maanas age = 5x and ravi age = 6x

• 5 years from now their ratio of age will be 6:7

•°• 5x + 5 = maanas age ..five year from now

6x + 5 = ravi age .. five year from now

therefore the condition will be apply like this:

(5x + 5)/(6x + 5) = 6/7

7(5x + 5) = 6(6x + 5)

35x + 35 = 36x + 30

35x - 37x = 30 - 35

-2x = -5

x = 5/2

Present age :

maanas age = 5x = 5× 5/2 = 25/2 = 12.5 years

ravi age = 6x = 6 × 5/2 = 30/2 = 15years

Answer 2

Let the present ages of Maanas and Ravi be x and y respectively.

Therefore ,

$\quad\bold{\frac{x}{y}=5:6}$

$\Rightarrow\bold{6x=5y}$

$\Rightarrow\bold{6x-5y=0}$

$\bold{\blue{\text{multipling both sides with 6}}}$

$\Rightarrow\bold{36x-30y=0}\qquad\qquad -eq1$

$\bold{\blue{\text{After five years }}}$

$\quad\bold{\frac{x+5}{y+5}=6:7}$

$\Rightarrow\bold{7(x+5)=6(y+5)}$

$\Rightarrow\bold{7x+35=6y+30}$

$\Rightarrow\bold{7x-6y=-5}$

$\blue{\bold{\text{multipling both sides with 5}}}$

$\quad\bold{35x-30y=-25}\qquad\qquad -eq2$

$\blue{\bold{\text{On subtracting eq2 from eq1 we get,}}}$

$\quad\bold{36x-30y-(35x-30y)=0-(-25)}$

$\Rightarrow\bold{36x-30y-35x+30y=25}$

$\Rightarrow\huge\bold{\green{\boxed{\red{x}=\pink{25}}}}$

$\blue{\bold{\text{On substituting the value of x in eq1}}}$

$\quad\bold{6x-5y=0}$

$\Rightarrow\bold{6(25)-5y=0}$

$\Rightarrow\bold{150-5y=0}$

$\Rightarrow\bold{-5y=-150}$

$\Rightarrow\bold{5y=150}$

$\Rightarrow\bold{y=\frac{150}{5}}$

$\Rightarrow\bold{y=\frac{\red{\cancel{\blue{150}}}^{\green{\:\:30}}}{\red{\cancel{\blue{\:\:\:5}}}}}$

$\Rightarrow\huge\bold{\green{\boxed{\red{y}=\pink{30}}}}$

Henceforth,

$\bold{\purple{present \:age\:of\:Maanas\:is}\:\pink{25\:years}}$

$\bold{\purple{present \:age\:of\:Ravi\:is}\:\pink{30\:years}}$