Useful for the students who prepare for numerical aptitude in recruitment process.

1. PROFIT & LOSS
STANDARD LEVEL
C.S.VEERARAGAVAN

2. COST PRICE A)₹ 300 B)₹ 350 C)₹ 375 D)₹ 400
Let the cost price of table = ₹ N
selling price with 15% gain = ₹
115N
100
CP = [(75%) x CP]/100 = ₹ 75N/100
New SP = ₹ (115N/100) – 60 AND
Profit 32%
115N
100
−60 −
75N
100
75N
100
X 100 = 32
115N
100
− 60 −
75N
100
=
32 N
100
∗
3
4
40N – 6000 = 24 N
16N = 6000
N = 375
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
SHORTCUT
GIVEN GAIN 15% = 100 + 15 = 115
CP = (100 – 25)% = 75
GIVEN PROFIT = 75% OF 32 = 24
DIFFERENCE = 115 – (75 + 24)
= 16
SOLD LESS = 60 * 100 = 6000
COST PRICE = 6000/16 = 375

3. COST PRICE
A)₹ 25 B)₹ 75
C)₹ 50 D)₹ 40
Let the cost price of first bicycle be ₹ P.
The cost price of second bicycle = ₹ (1600 - P)
[20% of P + 10% of (1600 - P )] - [10% of P +
20% of (1600 - P)] = 5
2P
10 +
1600 −P
10 −
P
10 +
2 1600 − P
10 = 5
P
10
−
1600 −P
10
= 5
⇒ 2P = 1600 + 50
∴ P = 1650/2 = 825
Cost of second bicycle = (1600 - 825) = ₹ 775
∴ Required difference = 825 - 775 = ₹ 50
A person bought two bicycles
for ₹ 1600 and
sold the first at 10% profit and
the second at 20% profit.
If he sold the first at 20% profit
and the second at 10% profit,
he would get ₹ 5 more.
The difference in the cost price
of the two bicycles was

4. SELLING PRICE
Cost of a packet of coffee powder
and a litre of milk
are ₹ 20 and ₹ 30 respectively.
10 cups of coffee is made with
one packet coffee powder and for
each cup 200 ml of milk is used.
If coffee is sold at 25% profit, the
selling price of each cup of coffee
is
A)₹ 12.50 B)₹ 6.25
C) ₹ 8 D)₹ 10
Cost of coffee powder used
in one cup = 20/10 = ₹ 2
Cost of milk used in one cup
= (30/1000) x 200 = ₹ 6
∴ Cost of each cup coffee
= 2 + 6 = ₹ 8
To gain 25% profit,
sale price of each cup of coffee
= 125% of 8
= ₹ 10

5. COST PRICE
A shopkeeper sells transistors at
15% above its cost price.
If he had bought it at 5% more
than what he paid for it
and sold it for ₹ 6 more, he would
have gained 10%.
The cost price of the transistor is ?
A)₹ 800 B)₹ 1000
C)₹ 1200 D)₹ 1400
Let cost price of transistor = ₹ N
According to the question,
CP of transistor = (N x 105)/100
SP of transistor = (115 x N)/100 + 6
Profit percentage = (SP - CP)/CP x100
115N
100
+ 6 −105N
100
105N
100
= 10
⇒ 10 = [(10N + 600) x 100]/ 105N
⇒ 105N = 100N + 6000
⇒ 5N = 6000
⇒ N= ₹ 1200

6. MAXIMUM PROFIT
Teenagers shoe company sells the shoes whose prices i.e.,cost price and
selling price are the multiples of either 13,14,15,16,17,18 or 19, starting
from Rs. 399 to Rs.699
(i.e, 399 ≤ CP/SP ≤ 699).
What can be the maximum profit of the company?
a)Rs. 292 b)Rs. 398 c)Rs. 298 d)Rs. 300
The maximum possible profit = maximum possible difference in SP and CP.
It means SP be maximum and CP be minimum
CP (min) = Rs. 399 19 x m = 399, where m is an integer.
Again SP (max) = Rs. 697, which is very close to 699
Here 697 = 17 k, k is a positive integer.
So, the maximum profit = 697 - 399 = Rs. 298

7. NET PROFIT / LOSS
Jhun Jhunwala makes 1000 toys and incurs a cost of Rs. 1.2 for each toy.
He marks-up the price in such a way that if he sells only 70% of
manufactured toys he will realize 16.66% overall profit.
He sells only 750 articles at the marked price since rest of the toys are
found to be defective so can't be sold.
What is the net profit or loss of Jhun Jhunwala?
a) 14.44% loss b)25% profit c)33.33% profit d)none of these
Total cost price = 1000 x 1.2 = Rs. 1200
Expected selling price = 700 x selling price per toys
= 1200 X 1.1666 = 1400
→ Selling price per toys = Rs. 2 per toy
Now the real selling price = 750 x 2 = Rs.1500
∴ Profit = (1500 - 1200) = Rs. 300
∴ Profit % = ( 300 / 1200 ) x 100 = 25%

8. Percentage Increase in CP
• A retailer increase the selling price by 25% due to which his profit
percentage increases from 20% to 25%.
• What is the percentage increase in cost price ?
• A)20% B)30% C)25% D)50%
• In beginning
Cost Price (CP) = Rs. 100 Profit % = 20 Selling Price (SP) =
120
When profit increases from 20% to 25%
Cost Price (CP) = y Profit % = 25
• Selling Price (SP) after 25% increase = 120 + 25% = Rs. 150
y + 25 % profit = 150
1.25 y = 150
so y = 120
% change in cost price = [ (120 - 100) / 100 ] x 100 = 20%

9. Successive discounts
The price of an article reduces to
576 after two successive
discounts.
The markup is 80% above the cost
price of Rs. 500.
What is the new profit percentage
if instead of two successive
discount
the markup price was further
increased successively two times
by the same percentage?
a)259.2% b)59.2%
c)159.2%
d)can’t be determined
Cost price (CP) = 500
Selling Price (SP) = 576
Markup price (MP) = 900
SP = MP 1 −
𝑅
100
2
576 = 900 1 −
𝑅
100
2
24 = 30 1 −
𝑅
100
1
Rate of Discount = 20%
New SP = 900 1 +
20
100
2
= 900 * (36/25)
= 1296
New Profit% =
1296 −500
500
∗100
= 796/5
= 159.2%

10. PERCENTAGE DISCOUNT
I wanted to purchase 10 chairs for
the class room whose cost was Rs.
200 each.
the trader offered me a discount if
I were to purchase a set of 12
chairs.
So I calculated that if I assume the
normal price of 10 chairs then
we can purchase 2 extra chairs
which cost me only Rs. 80 each of
two chairs at the cost price of 12
chairs after discount.
What is the percentage discount?
a)6% b)8%
c)12% d)10%
Price of 10 chairs = 10 x 200 = 2000
Price of 12 chairs (without discount)
= 12 x 200 = 2400
Price of 12 chairs (with discount)
= 10 x 200 + 2 x 80 = 2160
Therefore discount
= 2400 - 2160 = 240
Hence discount %
= (240 / 2400) x 100 = 10%

11. Profit % & Discount %
Cost price of 12 oranges is
equal to the selling price of 9
oranges and
the discount on 10 oranges is
equal to the profit on 5
oranges.
What is the percentage point
difference between the profit
percentage and discount
percentage?
A)20 B)22.22
C)16.66 D)15
Ratio of selling price and Cost Price,
SP:CP = 12:9 =4:3
Profit of 3 oranges = Re 1 (Let CP = Re 1)
Profit = 1/3 = 33.33%
and, Discount = 11.11%
Since, CP : SP : MP = 3 : 4 : 4.5
Profit doubles that of discount.
So, % point discount = 33.33%-11.11%
= 22.22% point.