Question

If a man sells the chair at 7% loss and table at 17% profit then he earns 296 as total profit but he sells the chair at 7% and table at 12% profit then he earns 400 as total profit. find the cost of table ​

Answer 1

Answer:-

Let the CP of chair be Rs. x and CP of table be Rs. y.

Given:

Case - 1 :-

Loss % on chair = 7 %

Profit% on table = 17 %

Total profit = Rs. 296

We know that,

• SP = (100 - loss% / 100) * CP.

So,

SP (chair) = (100 - 7/100) * x

⟶ SP (chair) = 93x/100

• SP = (100 + profit% / 100) * CP

⟶ SP (table) = (100 + 17 / 100) *y

⟶ SP (table) = 117y/100

We know,

Profit = SP - CP

So, 296 = SP of chair + SP of table - CP of chair - CP of table.

⟶ 296 = (93x/100) + (117y/100) - x - y

⟶ 296 = (93x + 117y - 100x - 100y)/100

⟶ 29600 = 17y - 7x -- equation (1)

Case - 2 :-

Profit % on chair = 7 %

⟶ SP (chair) = (100 + 7 / 100) * x

⟶ SP (chair) = 107x/100

Profit% on table = 12 %

⟶ SP (table) = (100 + 12 / 100) * y

⟶ SP (table) = 112y/100

Now,

Total Profit = 400

So ,

⟶ 400 = (107x/100) + (112y/100) - x - y

⟶ 400 = ( 107x + 112y - 100x - 100y)/100

⟶ 40000 = 7x + 12y -- equation (2)

Add equations (1) & (2).

⟶ 17y - 7x + 7x + 12y = 29600 + 40000

⟶ 29y = 69600

⟶ y = 69600/29

⟶ y = Rs. 2400

∴ CP of table is Rs. 2400.

Answer 2

Answer:

Let the Price of Chair be 100x and Price of Table be 100y

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\underline{\bf Statement\:\textit{1 :}}$

$:\implies\sf 7\%\:loss\:on\:chair+17\%\:profit\:on\:table=Rs.\:296\\\\\\:\implies\sf - (7\% \times 100x) + (17\% \times 100y) = 296\\\\\\:\implies\sf -7x + 17y = 296 \qquad eq. - 1$

$\underline{\bf Statement\:\textit{2 :}}$

$:\implies\sf 7\%\:profit\:on\:chair+12\%\:profit\:on\:table=Rs.\:400\\\\\\:\implies\sf (7\% \times 100x) + (12\% \times 100y) = 400\\\\\\:\implies\sf 7x + 12y = 400 \qquad eq. - 2$

⠀

$\underline{\bigstar\:\textsf{Adding eq. 1 and eq. 2 :}}$

$:\implies\sf-7x + 17y = 296\\\\:\implies\sf \:\:\:7x + 12y = 400 \\ \frac{ \qquad \qquad \qquad \qquad \qquad \quad}{} \\:\implies\sf (17y + 12y) = 296 + 400\\\\\\:\implies\sf 29y = 696\\\\\\:\implies\sf y = \dfrac{696}{29}\\\\\\:\implies\sf y = 24$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Cost of the Table :}}$

$\dashrightarrow\sf Table=100y\\\\\\\dashrightarrow\sf Table=100 \times 24 \\\\\\\dashrightarrow\underline{\boxed{\sf Table=Rs.\:2400}}$

⠀

$\therefore\:\underline{\textsf{Hence, Cost of the table is \textbf{Rs. 2400}}}.$