Profit and
Loss Practice Questions – Set 4
1. In an exhibition, Olive bought a painting for
Rs. 20000. She later sold it to Sarah for Rs. 23000. Sarah sold it to Heath for
double the profit percentage that Olive earned. At what price should Heath sell
this painting to earn 8% profit?
a) Rs.32292
b) Rs.28712
c) Rs.30000
d) Rs.32768
Answer: A)
Explanation: Olive bought a painting for Rs.
20000. She later sold it to Sarah for Rs. 23000.
We know, SP = CP × (1 +
Profit Percentage/100)
=> 23000 = 20000 × (1
+ Profit Percentage/100)
⇒ Profit percentage = 100 × (23000/20000 – 1) = 15
Sarah sold it to Heath
for double the profit percentage that Olive earned.
⇒ Sarah sold it to Heath at 30% profit.
Selling price for Sarah =
Cost price for Heath = 23000 × (1 + 30/100) = 29900
Now, Heath wants to earn
8% profit.
⇒ Selling price for Heath = 29900 × (1 + 8/100) = Rs. 32292
2. Srishti bought two hens for Rs. 1300. She sold
one at a loss of 5% and the other at a gain of 8%. What will be the cost price
of each hen respectively if she faced neither loss nor gain in this
transaction?
a) Rs.800, Rs.500
b) Rs.680, Rs.420
c) Rs.620, Rs.480
d) Rs.540, Rs.780
e) Rs.500, Rs.800
Answer: A)
Explanation: Let’s assume the cost price of first
hen to be Rs. x
And, the cost price of
second hen to be Rs. y
According to the given
information,
x + y = 1300
⇒ y = 1300 – x ------- Equation (1)
∵ first hen was sold at 5% loss,
Selling Price of first
hen = x – (5% of x) = 0.95x
∵ the second hen was sold at 8% profit,
Selling Price of second
hen = y + (8% of y) = 1.08y
∵ Neither profit nor loss was incurred in the entire
transaction, overall selling price must be equal to overall cost price.
⇒ 0.95x + 1.08y = 1300 ------- Equation (2)
Substituting the value of
y from Equation (1) into Equation (2), we get,
0.95x + 1.08(1300 – x) =
1300
⇒ 1.08x – 0.95x= 1404 – 1300
⇒ 0.13x = 104
⇒ x = 800
∴ y = 1300 – 800 = 500
3. The marked price of a cycle is Rs. 3200. A man
purchased it on two successive discounts of 8% and 10% and he spent Rs. 80 on
transportation and sold the cycle for Rs. 3200. What is the loss/gain
percentage of the man in selling the cycle?
a) 14.22%
b) Rs.17.23%
c) Rs.19.09%
d) Rs.23.32%
e) None of these
Answer: B)
Explanation: Marked price of a cycle = 3200 Rs
Two given successive
discounts on cycle are 8% and 10%,
Selling price of cycle
after successive discounts of 8% and 10%
= 3200 × 92/100 × 90/100
= 2649.6
Cost of cycle for the man
including transportation is
= 2649.6 + 80 = 2729.6
Gain of the man = 3200 –
2729.6 = 470 .4
Gain percentage =
470.4/2729.6 × 100 = 17.23%
4. A man invested in two investments in the ratio
of 4 : 3. If he loses 15% on first investment but gains 20% on the other
investment. What is the overall gain or loss caused to him?
a) 2.5%
b) 0%
c) 2%
d) 3%
e) 3.5%
Answer: B)
Explanation: Since the investments in first and
second scheme are in the ratio 4 : 3,
Let’s assume that the man
has invested Rs. 4x in first investment and Rs. 3x in second investment.
⇒ Total investment = Rs. 7x
∵ He loses 15% on first investment,
⇒ Final Amount = 4x – (15% of 4x) = 4x – (0.15 × 4x) = 3.4x
∵ he gains 20% on second investment,
⇒ Final Amount = 3x + (20% of 3x) = 3x + (0.2 × 3x) = 3.6x
⇒ Total final amount = 3.4x + 3.6x = 7x
∵ total final amount is the same as the total initial amount,
there’s no net loss or gain.
5. A man buys milk at a certain price per litre
and sells the mixture at the same rate after adding water to it. As to gain 30%
on his outlay, in what ratio he must mix water to milk. Assume that water is
free of cost.
a) 7 : 10
b) 3 : 10
c) 3 : 5
d) 5 : 9
e) 2 : 9
Answer: B)
Explanation: Let’s assume that the man buys milk
at Rs. x per litre
According to the given
information,
% Profit = 30
∴ Selling price of milk per litre = x + (30% of x) = 1.3x
∴ amount of milk available for Rs. x = (1/1.3) litres -----(i)
But since the selling
price of one litre of milk –water mixture is same as the cost price of one
litre of milk, one litre of mixture will be sold at Rs. x.
As we know from equation
(i), amount of milk in one litre of mixture = 1/1.3 lires
The rest must be water.
∴ Amount of water in 1 litre of mixture = 1 – (1/1.3) = (0.3/1.3)
Ratio of water to
milk = 0.3/1.3 : 1/1.3 = 3 : 10
6. A man who makes a profit of 25 % by selling
sugar at Rs. 4.50 a kg, lowers his price so as to gain only 30 Paisa per kg. In
what ratio must his sales increase so that his total profit may be the same as
before?
a) 1 : 3
b) 1 : 4
c) 1 : 5
d) 2 : 5
e) 1 : 2
Answer: A)
Explanation: By selling sugar at Rs 4.50 per kg
the man is making profit of 25% .
So the cost price of per
kg sugar = 4.5 × 100/125 = 3.60
By selling at Rs 4.50, he
is making profit of = (4.50 – 3.60) = 0.90 rupees = 90 paisa per kg
Suppose he sells X kg.
So total profit = 90X
paisa
Now if he lowered his
selling price and now he gains only 30 paisa profit per kg.
If he sells Y kg, then
total profit = 30 Y
In order to make the
profits same,
90X = 30 Y
⇒ 3X = y
⇒ X/Y =1/3
So Ratio of sale is 1:3
7. By selling chips for Rs. 153, Akash loses 10%.
For how much should he sell them to make a profit of 20%?
a) Rs.204
b) Rs.220
c) Rs.225
d) Rs.215
e) None of these
Answer: A)
Explanation: By selling chips for Rs. 153, Akash
loses 10%.
⇒ Selling Price = Cost Price - Loss = 153
⇒ Let the Cost price be Rs. x
⇒ x - 10% of x = 153
⇒ 0.9x = 153
⇒ x = 170
∴ In order to make a profit of 20%
⇒ Selling Price = Cost price + Profit
⇒ Selling price = 170 + 20% of 170
= 170 + 34 = Rs. 204
8. A merchant has 100 kg of sugar, part of which
he sells at 7% profit and the rest at 17% profit. He gains 10% on the whole.
How much is sold at 17%
a) 28kg
b) 30kg
c) 32kg
d) 25kg
e) 31kg
Answer: B)
Explanation: Say P is the Cost price of the sugar.
Total cost price = 100 ×
P
Say X kg is sold for 7%
profit
⇒ profit = (7/100) × Cost Price
⇒ Cost price of X kg = X × P
⇒ Selling price = 7/100 × (X × P) + (X × P) =
1.07XP
Similarly
SP of (100 – X) at 17% profit
= (100 × P
– X × P) × ((17/100) + 1) = 117P – 1.17P
Total selling price =
1.07XP + 117P – 1.17XP = 117P – 0.10XP
Total profit = Total
selling price – Total cost price = 117P – 0.10XP – 100P = 17P – 0.10XP
Profit percentage =
(Total profit/Cost price) × 100
Profit percentage =
[(17P – 0.10XP)/(100 × P)] × 100 = 10 ⇒ 17 – 0.10X = 10
⇒X = 7/0.1 = 70 kg
∴ 70 kg is sold at 7% profit and (100 – 70) = 30 kg is sold at 17% profit.
9. What is the gain percent, if bananas are bought
at 6 for 450P and sold at 5 for 525P?
a) 40%
b) 20%
c) 25%
d) 50%
e) None of these
Answer: A)
Explanation: CP of 6 banana = 450P
CP of 1 banana = 450P/6
SP of 5 banana = 525P
SP of 1 banana = 525P/5
Profit = SP – CP =
(525P/5 – 450P/6) = (3150P – 2250P)/30 = 900P/30 = 30P
Profit% = Profit/CP × 100
= [30P/(450P/6)] × 100 = 40%
10. Elsi buys an old phone for Rs. 4700 and spends
Rs. 800 on its repairs. If she sells the mobile for Rs. 5800, her gain percent
is:
a) 4 4/7%
b) 5 5/11%
c) 10%
d) 12%
e) 6 7/11%
Answer: B)
Explanation: Effective cost Price (C.P.) = Rs.
(4700 + 800) = Rs. 5500.
Selling Price (S.P.) =
Rs. 5800.
Gain = (S.P.) - (C.P.) =
Rs. (5800 - 5500) = Rs. 300.
Gain % = (300 ×
100)/5500% = 5 5/11%
