Profit and Loss
- A merchant buys p apples for ₹ q and sells q apples for ₹ p. If p < q, then in the whole outlay, he makes.
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Given,
CP of p apples = q
∴ CP of 1 apple = q/p
and SP of q apples = p
∴ SP of 1 apple = p/q
Given, p < q
∴ Loss = q/p - p/q = (q2 - p2) / pq
And Loss% = (Loss/CP) x 100Correct Option: B
Given,
CP of p apples = q
∴ CP of 1 apple = q/p
and SP of q apples = p
∴ SP of 1 apple = p/q
Given, p < q
∴ Loss = q/p - p/q = (q2 - p2) / pq
And Loss% = (Loss/CP) x 100
= {(q2 - p2)/pq} /(q/p)] x 100
= (q2 - p2)/q2 x 100
Therefore, when p < q , then the person had a loos which is given by
100 x (q2 - p2/q2)% loss.
- An article passing through two hands is sold at a profit of 40% at the original cost price. If the 1st dealer makes a profit of 20%, then the profit per cent made by the second is
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Let CP = ₹ 100
Then, SP = ₹ 140
Let the profit made by the 2nd dealer = N%
Then, (100 + N)% of 120% of ₹ 100 = ₹ 140
⇒ [(100 + N)/100 x (120/100) ] / 100 = 140Correct Option: B
Let CP = ₹ 100
Then, SP = ₹ 140
Let the profit made by the 2nd dealer = N%
Then, (100 + N)% of 120% of ₹ 100 = ₹ 140
⇒ [(100 + N)/100 x (120/100) ] / 100 = 140
⇒ 6(100 + N) = 700
⇒ 600 + 6N = 700
⇒ 6N = 100
∴ N = (100/6)% = (50/3) %
= 162/3
- A trader purchases a watch and a wall clock for ₹ 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earnes a profit of ₹ 51.50. The difference between the original prices of the wall clock and the watch is equal to
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Let cost price of a wall clock = ₹ N
∴ Cost price of a watch = ₹ (390 - N)
According to the question,
{(N x 10)/100} + {(390 - N) x 15}/100 = 51.50Correct Option: A
Let cost price of a wall clock = ₹ N
∴ Cost price of a watch = ₹ (390 - N)
According to the question,
{(N x 10)/100} + {(390 - N) x 15}/100 = 51.50
⇒ 390 x 15 - 5N = 51.50 x 100
⇒ 5N = 5850 - 5150 = 700
∴ N = 700/5 = 140
∴ Required difference = (390 - N) - N
= 390 - (2 x 140)
= 390 - 280 = 110
= ₹ 110
- A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
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Let the sugar sold at 8% gain = P
∴ Sugar sold at 18% gain = (1000 - P)
Let CP of sugar = ₹ Q per kg
Total CP = ₹ 1000 x Q
∴ [(108/100) x PQ)] + [(118/100) x (1000 - P) x Q]
= (114/100) x 1000 QCorrect Option: B
Let the sugar sold at 8% gain = P
∴ Sugar sold at 18% gain = (1000 - P)
Let CP of sugar = ₹ Q per kg
Total CP = ₹ 1000 x Q
∴ [(108/100) x PQ)] + [(118/100) x (1000 - P) x Q]
= (114/100) x 1000 Q
⇒ 108PQ + 118000Q - 118PQ = 114000Q
⇒ 10P = 4000
∴ P = 400
∴ Quantity sold at 18% profit = 1000 - 400 = 600 kg
- A person sold a table at a gain of 15%. Had he bought it for 25% less and sold it for ₹ 60 less, he would have made a profit of 32%. The cost price of table was
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Let the cost price of table = ₹ N
Then, selling price with 15% gain
= (100 + Gain%) x CP/100
= (100 + 15)% x CP/100
= (115 x N)/100 = ₹ 115N/100
Now CP = [(100 - 25%) x CP]/100 = ₹ 75N/100
New SP = ₹ (115N/100) - 60
Now, according to the question,
[[(115/100 )- 60) - (75N/100)]/ (75N/100)] x 100 = 32Correct Option: C
Let the cost price of table = ₹ N
Then, selling price with 15% gain
= (100 + Gain%) x CP/100
= (100 + 15)% x CP/100
= (115 x N)/100 = ₹ 115N/100
Now CP = [(100 - 25%) x CP]/100 = ₹ 75N/100
New SP = ₹ (115N/100) - 60
Now, according to the question,
[[(115/100 )- 60) - (75N/100)]/ (75N/100)] x 100 = 32
⇒ [[(115N - 6000 - 75N)/100 ]/ (75N/100)] x 100 = 32
⇒ [(40N - 6000)/75N] x 100 =32
⇒ (40N - 6000)/(3N x 4) = 32
⇒ 160N - 24000 = 96N
⇒ 160N - 96N = 24000
⇒ 64N = 24000
⇒ N = 24000/64
⇒ N = ₹ 375
∴ The cost price of table is ₹ 375.
