Question

22. Raju sold his car for 126,000 at a gain of 5%. In order to gain 10%, at what price should he sell the car?​

Answer 1

Answer:

He should sell the car for $132000.

Step-by-step explanation:

Given :

• Selling price of car is $126000.
• Gain Percent is 5%.

To find:

• Price should he sell the car for gain of 10% or Selling price of car for gain 10%.

Solution :

• We have to find selling price of car for gain Percent 10%. For this we need to find cost price first. For finding cost price we will use gain and gain percent formula. Formula is :

• Gain = Selling price (S.P) - Cost price (C.P)

→ Gain = 126000 - C.P

Gain Percent formula :

• $\pmb{\sf Gain\: Percent = \bigg( \dfrac{Gain}{C.P} \bigg) \times 100}$

Put, Gain Percent and gain in formula:

$\implies \sf 5 = \bigg( \dfrac{126000 - C.P}{C.P} \bigg) \times 100$

$\implies \sf 5 = \dfrac{12600000 - 100 C.P}{C.P}$

$\implies \sf 5 \times C.P = 12600000 - 100 C.P$

$\implies \sf 5 C.P + 100 C.P = 12600000$

$\implies \sf 105 C.P = 12600000$

$\implies \sf C.P = \dfrac{12600000}{105}$

$\implies \pmb{\sf C.P = 120000}$

Cost price of car is $120000.

• Finding selling price of car for gain 10%.

By using gain formula :

→ Gain = S.P - 120000

Now,

By using gain percent formula :

$\implies \sf 10 = \bigg( \dfrac{S.P - 120000}{120000} \bigg) \times 100$

$\implies \sf \dfrac{10}{100} = \dfrac{S.P - 120000}{120000}$

$\implies \sf \dfrac{10}{1\cancel{00}} \times 1200\cancel{00} = S.P - 120000$

$\implies \sf 12000 = S.P - 120000$

$\implies \sf 12000 + 120000 = S.P$

$\implies \pmb{\sf S.P = 132000}$

Therefore,

Selling price of car is $132000.

Answer 2

$\large{\dag \; {\underline{\underline{\red{\pmb{\sf{ \; Given \; :- }}}}}}}$

• Selling price of the car = Rs.126000
• Gain % = 5 %

$\\ \rule{200pt}{3pt}$

$\large{\dag \; {\underline{\underline{\color{darkblue}{\pmb{\sf{ \; To \; Find \; :- }}}}}}}$

• Selling price of the car to gain 10 % = ?

$\\ \rule{200pt}{3pt}$

$\large{\dag \; {\underline{\underline{\orange{\pmb{\sf{ \; Solution \; :- }}}}}}}$

$\maltese \; {\underline{\pmb{\frak{ Concept \; Used \; :- }}}}$

$\longrightarrow$ We will apply the concept of Profit % here .First, we will Calculate the cost price at which he bought the car . Next , we will the cost price of the car and again by using the formula for profit % we can calculate the selling price at which he shall sell the car to gain 10 % . Let's Solve :

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\pmb{\frak{ Formula \; Used \; :- }}}}$

• ${\underline{\boxed{\red{\sf{ Profit \; \% = \bigg\lgroup \dfrac{Profit}{Cost \; Price} \bigg\rgroup \times 100 }}}}}$

Where :

• Profit % = 5 %
• Profit = 126000 - Cost Price(C.P)
• Cost Price = ?

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\pmb{\frak{ Calculating \; the \; Cost \; Price \; :- }}}}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { Profit \; \% = \bigg\lgroup \dfrac{Profit}{Cost \; Price} \bigg\rgroup \times 100 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5 = \bigg\lgroup \dfrac{126000 - C.P}{Cost \; Price} \bigg\rgroup \times 100 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5 = \bigg\lgroup \dfrac{(126000 \times 100) - (C.P \times 100)}{Cost \; Price} \bigg\rgroup } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5 = \bigg\lgroup \dfrac{(126000 \times 100) - (C.P \times 100)}{Cost \; Price} \bigg\rgroup } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5 = \bigg\lgroup \dfrac{12600000 - 100C.P}{Cost \; Price} \bigg\rgroup } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5 \times C.P = 12600000 - 100C.P } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5C.P = 12600000 - 100C.P } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5C.P + 100C.P = 12600000 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 105C.P = 12600000 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { C.P = \dfrac{12600000}{105} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { C.P = \cancel\dfrac{12600000}{105} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; {\qquad{\purple{\sf { Cost \; Price = ₹ \; 120000 }}}} \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\pmb{\frak{ Calculating \; the \; Profit \; of \; 10 \; \% \; :- }}}}$

Here :

• Profit = Selling Price(S.P) - 120000
• Profit % = 10 %

$\begin{gathered} \; \implies \; \; \sf { Profit \; \% = \bigg\lgroup \dfrac{Profit}{Cost \; Price} \bigg\rgroup \times 100 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { 10 = \bigg\lgroup \dfrac{S.P - 120000}{120000} \bigg\rgroup \times 100 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { \dfrac{10}{100} = \bigg\lgroup \dfrac{S.P - 120000}{120000} \bigg\rgroup } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { \dfrac{10}{\cancel{100}} \times 1200\cancel{00} = S.P - 120000 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { 10 \times 1200 = S.P - 120000 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { 12000 = S.P - 120000 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; \sf { 12000 + 120000 = S.P } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; {\qquad{\pink{\sf { Selling \; Price = ₹ \; 132000 }}}} \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\maltese \; {\underline{\pmb{\frak{ Therefore \; :- }}}}$

❛❛ Selling price of the car should be ₹ 132000 to gain a profit of 10 % . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$