Question

A man bought a horse & a carriage for Rs. $ 60,000 $ . He sold the horse at $ 15\% $ profit and the carriage at a loss of $ 6\% $ . But still, he gained 1% overall. Find the cost price of horse

Answer 1

Hint: Here we will use the profit and loss formula. For Gain, the Selling Price should be greater than the Cost price whereas, for loss, selling price is less than Cost Price. For gain or loss, cost price is always taken as the base price for calculations.
 $
  Gain\% = \dfrac{{Gain \times 100}}{{C.P.}} \\
  Loss\% = \dfrac{{Loss \times 100}}{{C.P.}} \\
  $

Complete step-by-step answer:
Total cost price $ = 60,000 $
Horse selling profit $ \% = 15\% $
Carriage selling loss $ \% = 6\% $
 Net profit $ \% = 1\% $
 $
  Gain\% = \dfrac{{Gain \times 100}}{{C.P.}}\;{\text{ }}.....{\text{ (a)}} \\
  Loss\% = \dfrac{{Loss \times 100}}{{C.P.}}{\text{ }}.......{\text{(b)}} \\
  $
Let the cost price of a horse be $ x $ .
This means cost price of carriage is $ 60,000 - x $
Given in the question, profit percentage of horse $ = 15\% $
Putting values in equation (a) this means
\[\dfrac{{(S.P. - x) \times 100}}{x} = 15\% \]
Simplify the above equation –
\[(S.P. - x) \times 100 = 15x\]
Let selling price of horse be $ = S{P_1} $
 $ \Rightarrow S{P_1} = x + 0.15x = 1.15x{\text{ }}.....{\text{ (c)}} $
Again given in the question loss percentage of carriage $ = 6\% $
Let selling price of carriage be $ = S{P_2} $
Putting values in equation (b)
 $ \dfrac{{(60000 - x) - S{P_2}}}{x} \times 100 = 6\% $
Simplify the above equation
 $
\Rightarrow 60000 - x - S{P_2} = 0.06x \\
\Rightarrow S{P_2} = 60000 - 1.06x{\text{ }}....{\text{ (d)}} \;
  $
This means total selling price will be
 $ \Rightarrow SP = S{P_1} + S{P_2} $
 $ SP = 1.15x + 60000 - 1.06x $
Simplify the above equation
 $ SP = 60000 + 0.09x{\text{ }}.....{\text{ (e)}} $
Now again given in the question there is a net profit, so using equation (a)
 $
\Rightarrow \Pr ofit\% = \dfrac{{(SP - CP) \times 100}}{{C.P.}}\;{\text{ }} \\
\Rightarrow {\text{1% }} = \dfrac{{(SP - CP) \times 100}}{{C.P.}}\;{\text{ }} \;
  $
Using equation (e) this means:
 $ \dfrac{{60000 + 0.09x - 60000}}{{60000}} \times 100 = 1\% $
Simplify the above equation –
 $
\Rightarrow x = \dfrac{{60000}}{9} \\
\Rightarrow x = Rs.{\text{ }}6666.67 \;
  $
 cost price of carriage is $ 60,000 - x $
$\Rightarrow 60,000-6666.67 = 53,333.33$
So, the correct answer is “Hence the cost price of horse is Rs $ 6,666.67 $ and carriage is Rs. $ 53,333.33 $ ”.

Note: In such a problem we use the profit and loss formula to find the required. Correct formula and simplification should be done very carefully. For profit, the selling price should be greater than the cost price. For loss, the cost price should be greater than the selling price.The percentage value for profit and loss is calculated on the terms of cost price.