Question

Two horses were sold at Rs 12000 each, one at a loss of 20% and the other at a gain of 20%. The entire transaction resulted in
[a] No loss, No gain
[b] Loss of Rs 1000
[c] Gain of Rs 1000
[d] Gain of Rs 2000

Answer 1

Hint: Assume that the cost price of one horse is x and the other horse is y. Use the fact that 20% gain was obtained by selling the first horse to find the total cost price of the first horse. Use the fact that a total loss of 20% was suffered by selling the second horse to find the total cost price of the second horse. Hence find the total cost price of the two horses and the selling price of the two horses. Hence find the total loss or gain %age. Hence determine which of the options is correct.

Complete step by step answer:
Let the cost price of the first horse be y and that of the second horse be x.
Since an amount was lost by selling the second horse, we have
\[loss=x-12000\]
We know that $loss\%=\dfrac{loss}{c.p}\times 100$
Hence, we have
$20=\dfrac{x-12000}{x}\times 100$
Dividing both sides by 20, we get
$1=\dfrac{x-12000}{x}\times 5$
Multiplying both sides by x and using distributive property of multiplication over subtraction i.e. a(b-c) = ab-ac, we get
$x=5x-60000$
Subtracting x from both sides, we get
$4x-60000=0$
Adding 60000 on both sides, we get
$4x=60000$
Dividing both sides by 4, we get
$x=\dfrac{60000}{4}=15000$
Also, since we gained an amount by selling the first horse, we have
$gain=12000-y$
We know that $gain\%=\dfrac{gain}{c.p}\times 100$
Hence, we have
$20=\dfrac{12000-y}{y}\times 100$
Dividing both sides by 20, we get
$1=\dfrac{12000-y}{y}\times 5$
Multiplying both sides by y, we get
$y=60000-5y$
Adding 5y on both sides, we get
$6y=60000$
Dividing both sides by 6, we get
$y=10000$
Hence the cost price of the first horse is Rs 10,000 and that of second horse is Rs 15,000
Hence total cost price of the horses = 15000+10000 = Rs 25,000
Also, the total selling price of the horses is 12,000+12,000 = Rs 24,000
Hence the total loss suffered during the transaction is Rs 25000 – Rs 24000 =Rs 1000

So, the correct answer is “Option B”.

Note: Verification:
We can verify the correctness of our solution by checking that the loss suffered by selling one horse is 20% and that the gain gained by selling the other horse is 20%.
We have
Gain obtained by selling first horse = 12000-10000 = Rs 2000
Hence, we have
Gain% $=\dfrac{2000}{10000}\times 100=20$
Loss suffered by selling the second horse = 15000 – 12000 = Rs 3000
Hence, we have
Loss% $=\dfrac{3000}{15000}\times 100=20$
Hence our solution is verified to be correct.