Salil's age is 23 years more than half of the sangram's age.Fuve year'

1.	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.
Answer» 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.