Question

Five years ago, Namita was as old as Mamata. Ten years later, Namita will be twice as old as Mamta. How old is Mamta at present?

Answer 1

Answer:

Let present age of Namita be x and present age of Mamta be y.

★ 5 years ago :

\begin{gathered}\begin{lgathered}\bullet\:\:\textsf{Age of Namita = \textbf{(x - 5) years}}\\\bullet\:\:\textsf{Age of Mamta = \textbf{(y - 5) years}}\end{lgathered}\end{gathered}

Case 1 :-

Five years ago, Namita was thrice old as Mamta.

\begin{gathered}:\implies\sf x - 5 = 3 (y - 5) \\\\\\:\implies\sf x - 5 = 3y - 15\\\\\\:\implies\sf x = 3y - 15 + 5\\\\\\:\implies\sf x = 3y - 10\:\:\:\:\:\: \Bigg\lgroup \bf{Equation\:(1)}\Bigg\rgroup\end{gathered}:⟹x−5=3(y−5):⟹x−5=3y−15:⟹x=3y−15+5:⟹x=3y−10⎩⎪⎪⎪⎪⎪⎧Equation(1)⎭⎪⎪⎪⎪⎪⎫

★ 10 years later :

\begin{gathered}\begin{lgathered}\bullet\:\:\textsf{Age of Namita = \textbf{(x + 10) years}}\\\bullet\:\:\textsf{Age of Mamta = \textbf{(y + 10) years}}\end{lgathered}\end{gathered}

Case 2 :-

Ten years later, Namita will be twice as old as Mamta.

\begin{gathered}:\implies\sf x + 10 = 2 (y + 10) \\\\\\:\implies\sf x + 10 = 2y + 20\\\\\\:\implies\sf 3y - 10 + 10 = 2y + 20\:\:\:\:\:\: \Bigg\lgroup \bf{Putting\:the\:value\:of\:x\: from\:Equation\:(1)}\Bigg\rgroup\\\\\\:\implies\sf 3y = 2y + 20\\\\\\:\implies\sf 3y - 2y = 20\\\\\\:\implies\sf y = 20\:\:\:\:\:\: \Bigg\lgroup \bf{Mamta's\:age}\Bigg\rgroup \end{gathered}:⟹x+10=2(y+10):⟹x+10=2y+20:⟹3y−10+10=2y+20

MAMTA IS 20 YEARS OLD