One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{saving}}\,{\text{in}}\,{\text{N}}{\text{.S}}{\text{.C}}\,{\text{and}}\,{\text{P}}{\text{.P}}{\text{.F}}{\text{.}}\,{\text{be}}\, \cr & Rs.\,x\,{\text{and}}\,Rs.\,\left( {150000 - x} \right){\text{respectively}}. \cr & {\text{Then}},\,\frac{1}{3}x = \frac{1}{2}\left( {150000 - x} \right) \cr & \Rightarrow \frac{x}{3} + \frac{x}{2} = 75000 \cr & \Rightarrow \frac{{5x}}{6} = 75000 \cr & \Rightarrow x = \frac{{75000 \times 6}}{5} = 90000 \cr & \therefore {\text{Savings}}\,{\text{in}}\,{\text{Public}}\,{\text{Provident}}\,{\text{Fund}} \cr & = Rs.\,\left( {150000 - 90000} \right) \cr & = Rs.\,60000 \cr} $$