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 .
Answers
Answer: Rs. 2400
Step-by-step explanation:
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:-
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.
Hope it helps :)
Answer:
Let the Price of Chair be 100x and Price of Table be 100y
\underline{\bigstar\:\textsf{According to the given Question :}}
★According to the given Question :
\underline{\bf Statement\:\textit{1 :}}
Statement1 :
\begin{gathered}:\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\end{gathered}
:⟹7%lossonchair+17%profitontable=Rs.296
:⟹−(7%×100x)+(17%×100y)=296
:⟹−7x+17y=296eq.−1
\underline{\bf Statement\:\textit{2 :}}
Statement2 :
\begin{gathered}:\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\end{gathered}
:⟹7%profitonchair+12%profitontable=Rs.400
:⟹(7%×100x)+(12%×100y)=400
:⟹7x+12y=400eq.−2
⠀
\underline{\bigstar\:\textsf{Adding eq. 1 and eq. 2 :}}
★Adding eq. 1 and eq. 2 :
\begin{gathered}:\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\end{gathered}
:⟹−7x+17y=296
:⟹7x+12y=400
:⟹(17y+12y)=296+400
:⟹29y=696
:⟹y=
29
696
:⟹y=24
\rule{180}{1.5}
\underline{\bigstar\:\textsf{Cost of the Table :}}
★Cost of the Table :
\begin{gathered}\dashrightarrow\sf Table=100y\\\\\\\dashrightarrow\sf Table=100 \times 24 \\\\\\\dashrightarrow\underline{\boxed{\sf Table=Rs.\:2400}}\end{gathered}
⇢Table=100y
⇢Table=100×24
⇢
Table=Rs.2400
Hence, Cost of the table is Rs. 2400
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