Question

a man buys 2 pens and 4 pencils and gives a 100 rupee note to the shopkeeper. the shopkeeper asks him to pay 10 rupees more and take 4 pens and 2 pencils. how much would the man get back if he bought 2 pens and 3 pencils ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{price}\mathrm{of}\mathrm{pen}\mathrm{be}\mathrm{x}. \\ \mathrm{Price}\mathrm{of}\mathrm{pencil}\mathrm{be}\mathrm{y}. \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ 2\mathrm{x}+4\mathrm{y}=100...\left(1\right) \\ 4\mathrm{x}+2\mathrm{y}=100...\left(2\right) \\ \mathrm{Multiplying}\left(2\right)\mathrm{by}2\mathrm{and}\mathrm{sutracting}\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ 2\mathrm{x}-8\mathrm{x}=100-200 \\ -6\mathrm{x}=-100 \\ \mathrm{x}=\frac{100}{6} \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ 2\left(\frac{100}{6}\right)+4\mathrm{y}=100 \\ \frac{100}{3}+4\mathrm{y}=100 \\ 4\mathrm{y}=100-\frac{100}{3} \\ 4\mathrm{y}=\frac{200}{3} \\ \mathrm{y}=\frac{50}{3} \\ \mathrm{Now}, \\ \mathrm{Cost}\mathrm{of}2\mathrm{pens}\mathrm{and}3\mathrm{pencils}=2\left(\frac{100}{6}\right)+3\left(\frac{50}{3}\right) \\ =\frac{100}{3}+50 \\ =\frac{100+150}{3}=\frac{250}{3}=83.33 \\ \mathrm{Man}\mathrm{will}\mathrm{get}\mathrm{money}\mathrm{back}=100-83.33=\mathrm{Rs}.16.67\mathrm{ANS}... \end{gathered}$$