Question

A man sold a chair and table for 1246 rupees thereby making a profit of 25 %on the chair and 10% on the table . By selling them for 1339 rupees he would have realised a profit of 10% on the chair and 25% on the table .find the cost price of each.

Answer 1

$\huge\bold\orange{\underline{Solution:}}$

$\bold\green{\underline{Case-1:}}$

$\bold\purple{\underline{Given:}}$

The selling price of a chair and a table=Rs.1246

The profit on chair=25%

The profit on table=10%

$\bold\red{\underline{Let:}}$

The cost price of chair be X

The cost price of table be Y

Now, Solving we get, here

• using formula

$\bold\purple{\boxed{SP=\frac{100+G\%}{100}*CP}}$

⟹100+25/100×X+100+10/100×Y=1246

⟹125X/100+110Y/100=1246

⟹125X+110Y=124600

$\bold\purple{\boxed{125X+110Y=124600-----(1)}}$

$\bold\green{\underline{Case-2:}}$

The selling price a chair and a table=1339

The profit on chair=10%

The profit on table=25%

⟹100+10/100×X+100+25/100×Y=1339

⟹110X/100+125Y/100=1339

⟹110X+125Y=133900

$\bold\purple{\boxed{110X+125Y=133900-----(2)}}$

$\bold\red{\underline{A.T.Q}}$

Solving, equation 1 and 2 by multiplying and subtracting

⟹13750X+12100Y=13706000

⟹13750X+15625Y=16737500

⟹-3525Y=-303150

⟹Y=Rs.860

Putting the value of Y=860 in EQ 1

⟹125X+110Y=124600

⟹125X+110×860=124600

⟹125X+94600=124600

⟹125X=124600-94600

⟹125X=30000

⟹X=Rs.240

Hence,

The cost price of a chair=Rs.240

The cost price of table=Rs.860

$\large{\underline{\red{\rm{AnswEr:}}}}$

The cost price of chair=Rs.240

The cost price of table=Rs.860