Question

Question:

A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively. He gains 20% on the first motorcycle, 10% profit on the second and 25/8% loss on the total. Find the cost price of the third.

$\sf{dont \: spam}$
​

Answer 1

Answer:

Question :

A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively. He gains 20% on the first motorcycle, 10% profit on the second and 25/8% loss on the total. Find the cost price of the third.

$\begin{gathered}\end{gathered}$

Answer :

• ➤ The cost price of third motorcycle is Rs.6900.

$\begin{gathered}\end{gathered}$

Given :

• ➤ A trader sells three motorcycles for Rs 5400, Rs 3300 and Rs 5250 respectively.
• ➤ Trader gains 20% on the first motorcycle, 10% profit on the second and 25/8% loss on the total.

$\begin{gathered}\end{gathered}$

To Find :

• ➤ The cost price of third motorcycle.

$\begin{gathered}\end{gathered}$

Using Formulas :

${\longrightarrow{\small{ \underline{\boxed{\sf{C.P = \dfrac{100}{100 + Gain\%} \times S.P}}}}}}$

${\longrightarrow{\small{ \underline{\boxed{\sf{C.P = \dfrac{100}{100 - Loss\%} \times S.P}}}}}}$

• ⇢ C.P = Cost Price
• ⇢ S.P = Selling Price

$\begin{gathered}\end{gathered}$

Solution :

$\pink\bigstar$ Finding the cost price of first motorcycle :

• ⇢ S.P = Rs.5400
• ⇢ Gain% = 20%

${\longrightarrow \: \: {\sf{C.P = \dfrac{100}{100 + Gain\%} \times S.P}}}$

${\longrightarrow \: \: {\sf{C.P = \dfrac{100}{100 + 20} \times 5400}}}$

${\longrightarrow \: \: {\sf{C.P = \dfrac{540000}{120}}}}$

${\longrightarrow \: \: {\sf{C.P = \cancel{\dfrac{540000}{120}}}}}$

${\longrightarrow \: \: {\sf{\red{C.P = Rs.4500}}}}$

∴ The cost price of first motorcycle is Rs.4500.

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink\bigstar$ Finding the cost price of second motorcycle :

• ⇢ S.P = Rs.3300
• ⇢ Gain% = 10%

${\longrightarrow \: \: {\sf{C.P = \dfrac{100}{100 + Gain\%} \times S.P}}}$

${\longrightarrow \: \: {\sf{C.P = \dfrac{100}{100 + 10} \times 3300}}}$

${\longrightarrow \: \: {\sf{C.P = \dfrac{330000}{110}}}}$

${\longrightarrow \: \: {\sf{C.P = \cancel{\dfrac{330000}{110}}}}}$

${\longrightarrow \: \: {\sf{\red{C.P = Rs.3000}}}}$

∴ The cost price of second motorcycle is Rs.3000.

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink\bigstar$ Finding the cost price of third motorcycle :

• ⇢ Let the cost price of third motorcycle be Rs.x.

∴ The cost price of third motorcycle is Rs.x.

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink\bigstar$ Finding the total selling price of three motorcycles :

• ↠ S.P of first motorcycle = Rs.5400
• ↠ S.P of second motorcycle = Rs.3300
• ↠ S.P of third motorcycle = Rs.5250

${\longrightarrow \: \: \sf{Total \: S.P = 5400 + 3300 + 5250}}$

${\longrightarrow \: \:{\sf{\purple{Total \: S.P = Rs.13950}}}}$

∴ The total selling price of three motorcycles is Rs.13950.

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink\bigstar$ Finding the total cost price of three motorcycles :

• ↠ C.P of first motorcycle = Rs.4500
• ↠ C.P of second motorcycle = Rs.3000
• ↠ C.P of third motorcycle = Rs.x

$\longrightarrow \: {\sf{Total \: C.P = 4500 + 3000 + x}}$

$\longrightarrow \: {\sf{\purple{Total \: C.P = Rs.7500 + x}}}$

∴ The total cost price of three motorcycles is Rs.7500+x.

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink\bigstar$ Now,

• ⇢ Loss% = 25/8%
• ⇢ Selling Price = Rs.13900
• ⇢ Cost Price = 7500+x

We can see that the cost price is more than selling

• ⇢ C.P > S.P

${\longrightarrow \: \: {\sf{C.P = \dfrac{100}{100 - Loss\%} \times S.P}}}$

${\longrightarrow \: \: {\sf{7500 + x= \dfrac{100}{100 - \frac{25}{8}} \times 13950}}}$

${\longrightarrow \: \: {\sf{7500 + x= \dfrac{100 \times 13950}{ \frac{800 - 25}{8}}}}}$

${\longrightarrow \: \: {\sf{7500 + x= \dfrac{1395000}{ \frac{775}{8}}}}}$

${\longrightarrow \: \: {\sf{7500 + x= \dfrac{1395000}{775} \times 8}}}$

${\longrightarrow \: \: {\sf{7500 + x= \dfrac{1395000 \times 8}{775}}}}$

${\longrightarrow \: \: {\sf{7500 + x= \dfrac{11160000}{775}}}}$

${\longrightarrow \: \: {\sf{7500 + x= \cancel{\dfrac{11160000}{775}}}}}$

${\longrightarrow \: \: {\sf{7500 + x= 14400}}}$

${\longrightarrow \: \: {\sf{ x= 14400 - 7500}}}$

${\longrightarrow \: \: {\sf{\purple{ x= Rs.6900}}}}$

∴ The cost price of third motorcycle is Rs.6900.

$\begin{gathered}\end{gathered}$

Learn More :

$\boxed{\begin{minipage}{5cm}\bigstar \:\underline{\textbf{Profit and Loss Formulas :}}\\\\ \\ \sf {\textcircled{\footnotesize\textsf{1}}} \:S.P. = \sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times 100 \\\\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%} \\\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Profit = \sf \dfrac{Profit \% \times C.P.}{100} \\\\\\ \sf{\textcircled{\footnotesize\textsf{4}}} \: \:Profit (gain) = S.P. - C.P. \\\\\\\sf{\textcircled{\footnotesize\textsf{5}}} \: \: \sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{minipage}}$

$\rule{220pt}{3pt}$