question_answer 25)

                Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs. 50 per metre and trouser material that costs him Rs. 90 per metre. For every 2 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs. 36,600. How much trouser material did he buy?

Answer:

                Suppose that he bought x metres of trouser material. \[\because \]     For every 2 metres of trouser material, he buys = 3 metres of shirt material \[\therefore \] For every \[x\] metres of trouser material he buys \[=\frac{3x}{2}\] metres of shirt material \[\therefore \] Cost of trouser material \[=x\times 90\] \[=Rs.\,\,90x\] Cost of shirt material \[=\frac{3x}{2}\times 50\] \[=Rs.\,\,75x\] Profit of 10% on trouser material \[=\text{Rs}\,\text{90x}\,\times \,\frac{10}{100}=\text{Rs}\,9x\] Profit of 12% on shirt material \[=\text{Rs}\,75x\times \frac{12}{100}\,=Rs\,9x\] \[\therefore \] S.P. of trouser material \[=\text{Rs}\,90x+\text{Rs}9x\] \[=Rs.\,99x\] S.P. of shirt material \[=\text{Rs}\,75x+\text{Rs}9x\] \[=Rs.\,84\,x\] \[\therefore \] Total sale price = S.P. of trouser material + S.P. of shirt material \[=Rs\,99x+Rs\,84x\]                 \[=Rs.\,\,183\,x\] \[\because \]     His total sale is Rs 36,600 \[\therefore \] \[183x=36,600\] \[\Rightarrow \]               \[x=\frac{36600}{183}=200\]       | Dividing both sides by 183 Hence, he bought 200 m of trouser material. Check: \[\frac{3x}{2}=\frac{3}{2}\times 200=300\] \[\left( 200\times 90+200\times 90\times \frac{10}{100} \right)\] \[+\left( 300\times 50+300\times 50\times \frac{12}{100} \right)\] \[=(18000+1800)+(15000+1800)\] \[=19800+16800\] = 36600 Hence, the result is verified.