Question

A sold his car to B at a profit of 20% and B sold it to C at a profit of 10%. C sold it to D at a loss of 9.09%. D spent 10% of his purchasing price and then sold it at a profit of 8.33% to A once again. What is the loss of A?

1. 23%
2. 29%
3. 40%
4. 43%
5. 33%

Answer 1

Correct Answer - Option 4 : 43%

Given:

Profit % of A = 20%

Profit % of B = 10%

Loss % of C = 9.09%

Maintenance Cost for D = 10% of Purchasing Price

Profit % of D = 8.33%

Formula Used:

\({\rm{Selling\;price\;}}\left( {{\rm{S}}.{\rm{P}}.} \right) = {\rm{\;}}\frac{{\left( {100 \pm {\rm{Profit\;or\;loss}}} \right)\;\% }}{{100}}\; \times {\rm{Cost\;Price\;}}\left( {{\rm{C}}.{\rm{P}}.} \right)\)

\({\rm{Loss\;\% }} = \frac{{{\rm{Loss}}}}{{{\rm{Cost\;Price}}}}{\rm{\;}} \times 100\)

Calculation:

Let the Cost Price of Car for A be Rs.100 

\({\rm{S}}.{\rm{P}}.{\rm{\;of\;A}} = {\rm{\;}}\frac{{\left( {100 + 20} \right)}}{{100}}\; \times 100 = 120\) % MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb % a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr % 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape % WaaSaaa8aabaWdbmaabmaapaqaa8qacaaIXaGaaGimaiaaicdacqGH % RaWkcaaIYaGaaGimaaGaayjkaiaawMcaaaWdaeaapeGaaGymaiaaic % dacaaIWaaaaiaacckacqGHxdaTcaaIXaGaaGimaiaaicdacqGH9aqp % caaIXaGaaGOmaiaaicdaaaa!4756! \frac{{\left( {100 + 20} \right)}}{{100}}\; \times 100 = 120

\({\rm{S}}.{\rm{P}}.{\rm{\;of\;B\;}} = \frac{{\left( {100 + 10} \right)}}{{100}}\; \times 120 = \;132\)

\({\rm{S}}.{\rm{P}}.{\rm{\;of\;C}} = {\rm{\;}}\frac{{\left( {100 - 9.09} \right)}}{{100}}\; \times 132 = 120\)

Now, C.P. for D will be S.P. for C i.e.  Rs. 120

⇒ Actual C.P. for D = (Original C.P. + maintenance cost)

⇒ \({\rm{Actual\;C}}.{\rm{P}}.{\rm{\;for\;D\;}} = {\rm{\;}}120 + \frac{{10}}{{100}}\; \times 120 = 132\)

\({\rm{S}}.{\rm{P}}.{\rm{\;for\;D}} = {\rm{\;}}\frac{{\left( {100 + 8.33} \right)}}{{100}}\; \times 132 = 143\)

S.P. for D will be C.P. for A i.e. ₹143.

Loss = (New C.P. of A – original C.P. of A)

⇒ Loss = (143 – 100) = 43

\({\rm{Loss\;\% }} = \frac{{43}}{{100}}\; \times 100 = 43\% \)

∴ Loss Percent of A is 43%.