Question

Salil's age is 23 years more than half of the sangram's age.Fuve year's ago, the sum of their age was 55 years.Find their present ages.
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Answer 1

Answer:

The present ages of Salil and Sangram are 37 years and 28 years respectively.

Step-by-step-explanation:

Let Sangram's present age be x years.

From the first condition,

Salil's age = Half of Sangram's age + 23

$\displaystyle{\implies\sf\:Salil's\:present\ age\ =\:\dfrac{x}{2}\:+\:23}$

$\displaystyle{\implies\sf\:Salil's\:present\ age\ =\:\dfrac{x\:+\:2\:\times\:23}{2}}$

$\displaystyle{\sf\:\therefore\:Salil's\:present\ age\ =\ \dfrac{x\ +\ 46}{2}\ years}$

Now,

Sangram's age five years ago = ( x - 5 ) years

And Salil's age five years ago = $\displaystyle{\sf\:\dfrac{x\:+\:46}{2}\:-\:5\ years}$

From the second condition,

$\displaystyle{\sf\:(\:x\:-\:5\:)\:+\:\left(\:\dfrac{x\:+\:46}{2}\:-\:5\:\right)\:=\:55}$

$\displaystyle{\implies\sf\:x\:-\:5\:+\:\dfrac{x\:+\:46}{2}\:-\:5\:=\:55}$

$\displaystyle{\implies\sf\:x\:+\:\dfrac{x\:+\:46}{2}\:-\:5\:-\:5\:=\:55}$

$\displaystyle{\implies\sf\:\dfrac{2x\:+\:x\:+\:46}{2}\:-\:10\:=\:55}$

$\displaystyle{\implies\sf\:\dfrac{3x\:+\:46}{2}\:-\:10\:=\:55}$

$\displaystyle{\implies\sf\:\dfrac{3x\:+\:46}{2}\:=\:55\:+\:10}$

$\displaystyle{\implies\sf\:\dfrac{3x\:+\:46}{2}\:=\:65}$

$\displaystyle{\implies\sf\:3x\:+\:46\:=\:65\:\times\:2}$

$\displaystyle{\implies\sf\:3x\:+\:46\:=\:130}$

$\displaystyle{\implies\sf\:3x\:=\:130\:-\:46}$

$\displaystyle{\implies\sf\:3x\:=\:84}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{84}{3}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:28}}}}$

∴ The present age of Sangram is 28 years. ─────────────────────

Now,

$\displaystyle{\sf\:Salil's\:present\ age\ =\ \dfrac{x\ +\ 46}{2}\ years}$

$\displaystyle{\implies\sf\:Salil's\:present\ age\ =\:\dfrac{28\:+\:46}{2}}$

$\displaystyle{\implies\sf\:Salil's\:present\ age\ =\ \cancel{\dfrac{74}{2}}}$

$\displaystyle{\implies\boxed{\red{\sf\:Salil's\:present\ age\ =\:37\:years\:}}}$

∴ The present age of Salil is 37 years.