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

1. PERCENTAGE –
STANDARD LEVEL
C.S.VEERARAGAVAN
APT TRAINER

2. ADDED TO INCREASE %
• An alloy of gold and silver weights 50g.
• It contains 80% gold.
• How much gold should be added to the alloy,
so that percentage of gold is increased to 90 ?
a)50g b)60g c)30g d)40g
Gold in 50g of alloy = (80 x 50)/100 = 40 g
Let W gram gold must be added.
40 + 𝑊
50 + 𝑊
=
90
100
100(40 + W) = 90 (50 + W)
10W = 4500 – 4000 = 500
W = 50g

3. • In a test, Rajesh got 112 marks which was 32 more than the passing
marks.
• Sonal got 75% marks which was 70 more than the passing marks.
• What is the minimum passing percentage of the test. ?
A)35% B)45% C)40% D)48%
Let maximum marks be N .
75𝑁
100
- 70 = 112 – 32
75𝑁
100
= 80 + 70
∴ N = 200
Passing marks = 112 - 32 = 80
(as Rajesh got 112 marks which is 32 more than the passing marks)
∴ Minimum passing marks percentage = (80/200) x 100%
= 40%

4. Ram sells his goods 25% cheaper then Shyam and 25% dearer
than Hari.
How much percentage is Hari's goods cheaper than Shyam ?
A)25 B)331/3 C)40 D)50
Let the selling price of goods by shyam be = ₹ 100
∴ Selling price of goods by Ram = ₹ 75
125% of selling price of goods by Hari = 75
Selling price of goods by Hari = (100/125) x 75 = ₹ 60
So, Hari's goods are cheaper than shyam's good by
(40/100) x 100% = 40%

5. The ratio of the number of boys and girls in a school is 3 : 2.
If 20% of the boys and 25% of the girls are scholarship holders, then
the percentage of the students who do not get the scholarship, is ?
a)78% b)75 % c)60% d)55%
Let number of boys be 300.
Number of girls = 200
Boys holding scholarship = (20/100) x 300 = 60
Girls holding scholarship = (25/100) x 200 = 50
Total student holding scholarship = 60 + 50 = 110
Percentage of students not holding scholarship =
500 −110
500
∗100
=
390
500
∗100
= 78%

6. The price of ghee is increased by 32%.
Therefore, a family reduces its consumption, so that the increment in price
of ghee is only 10%.
If consumption of ghee is 10 kg before the increment, then What is the
consumption now ?
a)81/3 kg b)83/4 kg c)81/2 kg d)9 kg
Let price of ghee before increment = ₹ N
Consumption = 10 kg
Then, expenditure on ghee = ₹ 10N
After increment,
Expenditure on ghee = 110% of 10N = 11N
Price of ghee = 132% of N = (N x 132)/100 = 33N/25 per kg
∴ Now consumption = (11N x 25) / 33N kg
= 81/3 kg

7. The expenses on wheat, meat
and vegetable of a family are
in the ratio 12 : 17 : 3.
The prices of these articles
are increased by 20%, 30%
and 50% respectively,
The total expenses of the
family on these articles are
increased by ?
a)231/3% b)281/8%
c)271/8% d)251/7%
Let expenses on wheat be 12N.
Expenses on meat = 17N.
Expenses on vegetables = 3N.
∴ Total expenses = 32N.
Increased expenses
=(120% of 12N) + (130% of 17N) + (150% of 3N)]
= ₹
120
100
∗ 12N +
130
100
∗ 17N +
150
100
∗ 3N
= ₹ [
72N
5
+
221N
10
+
9N
2
]
= ₹
144N + 221N + 45N
10
= ₹ 410N/10 = ₹ 41
Total increase percentage = (9N/32N) x 100 %
= 225/8 % = 281/8%

8. In 1998, ratio of the numbers
of students taking
examinations in x and z states
are respectively 3 : 5 : 6.
Next year, the numbers of
students are increased by 20%,
10% and 20% respectively.
If ratio of the numbers of
students in states x and z is 1 :
2, then find the number of
students who sit to take
examination in 1998. ?
a)5000 b)6000
c)75000 d)Data is insuffcient
In 1998
Let number of students in x = 3k
Number of students in y = 5k and
Number of students in z = 6k
Next year,
number of students in x = 3k + 20% of 3k
= 18k/5
Number of students in y = 5k + 10% of 5k
= 11k/2
Number of students in z = 6k + 20% of 6k
= 36k/5
According to the question,
(18k/5) / (36k/5) = 1/2
Thus, data is insufficient.

9. • In a examination out of 480
students, 85% of the girls
and 70% of the boys
passed.
• How many boys appeared
in the examination,
• if total pass percentage
was 75% ?
a)370 b)340
c)320 d)360
Total number of students = 480
percentage of total students passed
= 75% of total student
= (75 x 480)/100 = 360 students
Let the number of boys be N
Then, 70% of N + 85% of (480 - N) = 360
[(70 x N)/100] + [85 x (480 - N)]/100 = 360
70N - 85N + 40800 = 36000
40800 - 36000 = 85N - 70N
4800 = 15N
N = 4800/15 = 320

10. • A jogger desires to run a certain course in 1/4 less time than
he usually takes.
• By What per cent must be increase his average running speed
to accomplish the goal ?
a)50% b)20% c)25% d)331/3%
Let usual speed and usual time taken by the jogger are D and T,
respectively. Let his new speed be D'.
Then, DT = (3D'/4)T
⇒ D = 3D'/4
⇒ D' = 4D/3
Thus, he has to increased his speed by [(4D/3 - D) / D] x 100% .
= 331/3 %