Question : A man bought a horse and a carriage for Rs. 40,000. He sold the horse at a gain of 10% and the carriage at a loss of 5%. He gained 1% on his whole transaction. The cost price of the horse was:
Option 1: Rs. 15,000
Option 2: Rs. 16,000
Option 3: Rs. 18,000
Option 4: Rs. 20,000
Correct Answer: Rs. 16,000
Solution :
Let the cost price of the horse as $\mathrm{H}$ and the cost price of the carriage as $\mathrm{C}$.
Given that the man bought a horse and a carriage for $\mathrm{Rs.}\;40,000$.
$\mathrm{H + C }= 40,000$____(i)
The man sold the horse at a gain of $10\%$, so the selling price of the horse was $\mathrm{1.1H}$.
Also, he sold the carriage at a loss of $5\%$, so the selling price of the carriage was $\mathrm{0.95C}$.
Given that he gained $1\%$ on the whole transaction,
The total selling price $=1.01\mathrm{(H + C)} = 1.01 \times 40000 = \mathrm{Rs.}\;40,400$
$⇒\mathrm{1.1H + 0.95C} = 40,400$____(ii)
From equation (i),
$⇒\mathrm{C = 40000 - H}$
Substituting this into the second equation,
$⇒\mathrm{1.1H + 0.95(40000 - H) = 40,400}$
$⇒\mathrm{0.15H=2,400}$
$⇒\mathrm{H =16,000}$
Hence, the correct answer is Rs. 16,000.
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