Percentage
solutions:
Practice
1:
1.
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
=
110 - (60)
=
50.
|
Required
percentage =
|
|
50
|
x
100
|
%
= 45
|
5
|
%
|
|
110
|
11
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2. Let
their marks be (x +
9) and x.
|
Then, x +
9 =
|
56
|
(x +
9 + x)
|
|
100
|
25(x +
9) = 14(2x +
9)
3x =
99
x =
33
So,
their marks are 42 and 33.
3.
Suppose originally he had x apples.
Then,
(100 - 40)% of x =
420.
|
|
60
|
x x =
420
|
|
100
|
|
x =
|
|
420
x 100
|
=
700.
|
|
60
|
4. Clearly,
the numbers which have 1 or 9 in the unit's digit, have squares that
end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21,
29, 31, 39, 41, 49, 51, 59, 61, 69.
Number
of such number =14
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Required
percentage =
|
|
14
|
x
100
|
%
= 20%.
|
|
70
|
5. Answer: Option E
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x%
of y =
|
|
x
|
x y
|
|
=
|
|
y
|
x x
|
|
= y%
of x
|
|
100
|
100
|
A
= B.
6. Answer: Option A
|
20%
of a = b
|
20
|
a = b.
|
|
100
|
|
b%
of 20 =
|
|
b
|
x
20
|
|
=
|
|
20
|
a x
|
1
|
x
20
|
|
=
|
4
|
a =
4% of a.
|
|
100
|
100
|
100
|
100
|
7. Answer: Option E
Let
the number of students be x.
Then,
Number
of students above 8 years of age = (100 - 20)% of x =
80% of x.
|
80%
of x =
48 +
|
2
|
of
48
|
|
3
|
|
|
80
|
x =
80
|
|
100
|
x =
100.
8. Answer: Option D
Let
the number be x.
|
Then,
error =
|
5
|
x -
|
3
|
x =
|
16
|
x.
|
|
3
|
5
|
15
|
|
Error%
=
|
|
16x
|
x
|
3
|
x
100
|
%
= 64%.
|
|
15
|
5x
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|||||
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9.
Answer: Option A
Number
of valid votes = 80% of 7500 = 6000.
Valid
votes polled by other candidate = 45% of 6000
|
=
|
|
45
|
x
6000
|
|
=
2700.
|
|
100
|
10.
Answer: Option A
Total
number of votes polled = (1136 + 7636 + 11628) = 20400.
|
Required
percentage =
|
|
11628
|
x
100
|
%
= 57%.
|
|
20400
|
11. Answer: Option C
Let
the amount taxable purchases be Rs. x.
|
Then,
6% of x =
|
30
|
|
100
|
|
x =
|
|
30
|
x
|
100
|
=
5.
|
|
100
|
6
|
Cost
of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70
12. Answer: Option A
|
Rebate
= 6% of Rs. 6650 = Rs. |
|
6
|
x
6650
|
|
=
Rs. 399.
|
|
100
|
|
Sales
tax = 10% of Rs. (6650 - 399) = Rs.
|
|
10
|
x
6251
|
|
=
Rs. 625.10
|
|
100
|
Final
amount = Rs. (6251 + 625.10) = Rs. 6876.10
13. Answer: Option B
Increase
in 10 years = (262500 - 175000) = 87500.
|
Increase%
=
|
|
87500
|
x
100
|
%
= 50%.
|
|
175000
|
|
Required
average =
|
|
50
|
%
= 5%.
|
|
10
|
Practice 2
- 1/5 X 2/5 X a = ¼ X a X b => b = 8/25
- % difference = (200-50)/50 X 100 = 300 %
- % increase = (80-30)/30 X 100 = 166.66 %
- 1.3 x = 78000 => x = 60000.
- Net effect = 1.2 X 1.1 X 0.7
0.924
=> 7.6% decrease.
- Let I be the income.
Expenditure
= 0.8I
Savings
= 0.2I => 20%
New
income = 1.2I (since 20% rise)
New
expenditure = (0.8I) X 1.3 (Since 30% rise)
=
1.04I
So,
new savings = 1.2I – 1.04I = 0.16I
=>
16%
(So
income decreased form 20% to 16%)
%
decrease = (20-16)/20 X 100 = 20%.
- It is equivalent to 1.25 decreased to 1.
%
decrease = (1.25-1)/1.25 X 100 = 20%
8.
% change in area = 1.2 X 1.2 (since area = side X side)
=
1.44 => 44%.
- It is equivalent to 1.25 decreased to 1. So 20% decrease.
- Valid Votes:
A
got 56% => B got 44%
Difference
= 12% = 48000
So,
100% = 400000. These are valid votes.
But
valid votes are only 80% of total votes.
So,
80% of total votes = 400000 => total votes =
500000
- Total money = Rs. 300.
Saving
of the lady = 10% of 300 = 30/-
With
30/- she bought 5 kg sugar => each kg costs Rs. 6/-
- In 20lt, salt = 20% => 4 lt.
New
volume = 18 lt (2 lt evaporated)
So,
new % = 4/18 X 100 = 22.22%
- % correction = (58-46.4)/58 X 100 = 20%
- Three successive decreases of 20%, 20% and 10%
=>
0.8 X 0.8 X 0.9 = 0.576
Again
10% decrease =>
0.576
– 0.1 = 0.476.
So,
0.476 x = 9520 => x = 20000.
- Total discount = 0.9 X 0.8 X 0.7 = 0.504 of actual price.
So,
price = 0.504 X 10000 = 5040.
- In 10 lt, alcohol is 10% = 1 lt.
Let
x lt alcohol is added.
So,
(1+x)/(10+x) = 20% = 1/5 => x = 1.25 lt.
- A = 2B and B = 3C (ince 200% more)
A
= 6C => 500 % more.
- 50% of max marks – 40% of max marks = 25
max
marks = 250
Pass
marks = 40% of max + 10 => 100 + 10 = 110.
- A = 1.2 B => B = A/1.2 => 0.8333A => 16.66%.
(OR)
Decrease from 1.2 to 1 => 16.66%.
- 1.1 X 1.1 X x = 12100 => x = 10000.
- Salt = 15% of x = 0.15x (x = volume of solution)
Now,
0.15x/(x-30) = 20% = 1/5 (since 30 lt evaporated)
x
= 120
- 20% empty => 80 % full = 240 lt => 20% = 60
- A => 1.4 X 1.4 = 1.96
B
=> 1.9 => 6% difference.
24.
From 1960 to 1975, in 15 years population doubled every 5 yrs =>
three times
So,
2 X 2 X 2 = 8 times => 700% more.
- [(75% X 60) + (x% X 20)] / 80 = 80% => x = 95. (since required is 80%)
(OR)
60 out of 80 is 3/4. So, (3/4 X 75) + (1/4 X x)
= 80 => x =95.
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