Math, asked by nunu3345, 9 months ago

The ratio of present ages of P and Q is 5 : 8. Three years later their ages will be in ratio 8 : 11. What is the present age (in years) of Q?

A) 5 B) 11 C) 14 D) 8

Answers

Answered by Anonymous
3

Given:

Ratio of present ages of P & Q is 5:8.

Three yrs. hence ratio of their ages will be 8:11.

To Find:

The present ages of P & Q .

Solution:

Let us take ratio of present ages be 5x:8x .

So, After 3 yrs,

  • Age of P = 5x+3
  • Age of Q = 8x+ 3 .

So, Ratio will be , 5x+3/8x+3 .

But it is given 8:11.

So,ATQ,

\sf{\implies\dfrac{5x+3}{8x+3}=\dfrac{8}{11}}

\sf{\implies 11(5x+3) = 8(8x+3)}

\sf{\implies 55x+33=64x+24}

\sf{\implies 55x-64x=24-33}

\sf{\implies -9x=-9}

\sf{\implies x =\dfrac{-9}{-9}}

\sf{\implies x =\cancel{\dfrac{-9}{-9}}}

{\underline{\boxed{\red{\bf{\leadsto x =1}}}}}

So,

  1. Age of P = 5x =5×1 =5years.
  2. Age of Q = 8x =8×1=8years.

Answered by Anonymous
3

Answer:-

\sf{A) \ 5 \ is \ the \ correct \ option.}

Given:

  • \sf{The \ ratio \ of \ present \ ages \ of }
  • \sf{P \ and \ Q \ is \ 5:8.}

  • \sf{After \ three \ years \ ratio \ of \ their \ ages}
  • \sf{will \ be \ 8:11.}

To find:

\sf{Present \ age \ of \ Q.}

Solution:

\sf{Let \ the \ constant \ be \ x.}

\sf{According \ to \ the \ first \ condition.}

\sf{Age \ of \ P=5x}

\sf{Age \ of \ Q=8x}

\sf{According \ to \ the \ second \ condition.}

\sf{\frac{5x+3}{8x+3}=\frac{8}{11}}

\sf{\therefore{11(5x+3)=8(8x+3)}}

\sf{\therefore{55x+33=64x+24}}

\sf{\therefore{64x-55x=33-24}}

\sf{\therefore{9x=9}}

\sf{\therefore{x=\frac{9}{9}}}

\sf{\therefore{x=1}}

\sf{Present \ age \ of \ Q=8(1)=8 \ years.}

\sf\purple{\tt{\therefore{The \ present \ age \ of \ Q \ is \ 8 \ years.}}}

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