Question

Five years ago, Namita was thrice as old as Mamta,
Ten years later, Namita will be twice as old as Mamta. How old is Mamta at present?
(A) 50 years
(B)20 years
(C) 30 years
(D)15 years​

Answer 1

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

★ 5 years ago :

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

Case 1 :-

Five years ago, Namita was thrice old as Mamta.

$:\implies\sf x - 5 = 3 (y - 5) \\\\\\:\implies\sf x - 5 = 3y - 15\\\\\\:\implies\sf x = 3y - 15 + 5\\\\\\:\implies\sf x = 3y - 10\:\:\:\:\:\: \Bigg\lgroup \bf{Equation\:(1)}\Bigg\rgroup$

★ 10 years later :

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

Case 2 :-

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

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

$\therefore\:\underline{\textsf{Present age of mamta is \textbf{20 years}}}.</p><p>$

Answer 2

Answer:

(B) 20 years

Step-by-step explanation:

Five years ago, Namita was thrice as old as Mamta.

Assume that the age of Namita is x years and Mamta is y years.

As per given condition,

→ (x - 5) = 3(y - 5)

→ x - 5 = 3y - 15

→ x = 3y - 10 .............(1)

In another part of the question we have given that, Ten years later, Namita will be twice as old as Mamta.

As per given condition,

→ (x + 10) = 2(y + 10)

→ x + 10 = 2y + 20

→ x = 2y + 10 .............(2)

On comparing (1) & (2) we get,

→ 3y - 10 = 2y + 10

→ y = 20

→ y = 20

Present age of Mamta is 20 years.

Substitute value of y in (1)

→ x = 3(20) - 10

→ x = 60 - 10

→ x = 50

Present age of Namita is 50 years.