Percentage - Aptitude MCQ Questions and Solutions with Explanations

61

A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people, the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people be solicited?

A) 300 B) 250 C) 400 D) 500

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the number of people be x who has been asked for the donations
People already solicited = 60% of x = 0.6x
Remaining people = 40% of x = 0.4x
Amount collected from the people solicited,
= 600 × 0.6x = 360x
360x = 75% of the amount collected
Remaining amount = 25% = 120x
Thus,
Average donations from remaining people,
$$\eqalign{ & = \frac{{120{\text{x}}}}{{0.4{\text{x}}}} \cr & = 300 \cr} $$

62

In the Bombay Stock Exchange there are 45% female employees and thus the number of male employees is exceeded by 72. Hence the total no. of employees in the BSE is:

A) 540 B) 720 C) 800 D) 550

Discuss

Answer & Solution

Answer: Option B

Solution:

Female employees = 45%
Male employees = 55%
Difference = 55 - 45 = 10%
→ 10% = 72
→ 1% = $$\frac{{72}}{{10}}$$
→ 100 = 7.2 × 100 = 720

63

The average weight of a class of students is 67.5 kg. The weight of the class teacher is 25% more than the average weight of the class. The average weight of the class is less than the class teacher by x%. The value of x is:

A) 33.335 B) 25% C) 20% D) 22%

Discuss

Answer & Solution

Answer: Option B

Solution:

100 == 25% ↑ ==> 125 == x%↓ ==> 100
$${\text{x}}\% = \frac{{25 \times 100}}{{100}} = 25\% $$
We don't need the actual value to calculate the answer

64

Every day a mango seller sells half his stock, 10% of the stock overnight gets spoiled. If 1983 mangoes rotted over 3 nights then how many did hi start with on the first day ?

A) 25,000 B) 24,000 C) 30,000 D) 32,000 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Day	1	2	3
Initial mangoes	x (let)	0.45x	0.2025x
Sales	0.5x	0.225x	0.10125x
Over night remaining	0.5x	0.225x	0.10125x
Rotten	0.05x	0.0225x	0.010125x
Next day stock	0.45x	0.2025x

Thus, Total mangoes rotten amount is
⇒ 0.05x + 0.0225x + 0.010125x = 0.082625x = 1983
x = 24,000

65

In a factory there are three types of machine M₁, M₂ and M₃ which produces 25%, 35% and 40% of the total products respectively. M₁, M₂ and M₃ produces 2%, 4% and 5% defective products, respectively. what is the percentage of non-defective products ?

A) 89% B) 97.1% C) 96.1% D) 86.1% E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Non-defective products M¹ = 25 × 0.98 = 24.5%
Non-defective products M² = 35 × 0.96 = 33.6%
Non-defective products M³ = 40 × 0.95 = 38%
Percentage of non-defective products
= 24.5 + 33.6 + 38
= 96.1%

66

The square of a positive number is 2000% greater than the number itself, then the square of that number is :

A) 1762 B) 1635 C) 441 D) 139

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & {\text{Let the positive number be x}}. \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & x \times x = x + \frac{{\left( {x \times 2000} \right)}}{{100}} \cr & {x^2} = x + 20x \cr & {x^2} - 21x = 0 \cr & {\text{Either}}, \cr & x = 0,\,\,or \cr & x = 21 \cr & {\text{21}}\,{\text{is}}\,{\text{the}}\,{\text{possible}}\,{\text{value}}{\text{.}} \cr & {\text{Then}}\,{\text{square}}\,{\text{of}}\,21\,{\text{is}}\,441 \cr} $$

67

The cost of a car is 400% greater than the cost of a bike. If there is an increase in the cost of the car is 15% and that of bike 20%. Then the total increase in the cost of the 5 cars and 10 bikes is:

A) 17.5% B) $$16\frac{3}{7}$$ % C) 18.5% D) 18.25%

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the bike's initial cost be x and then car's initial cost be 5x
After the increase,
Bike price = 1.2x
Car price = 5.75x
Initial total cost of 5 cars and 10 bikes,
= 25x + 10x = 35x
New cost,
= 28.75x + 12x = 40.75x
Change in cost = (40.75x - 35x) = 5.75x
% change = $$\frac{{5.75{\text{x}} \times 100}}{{35}} = 16\frac{3}{7}\% $$

68

Connie has a number of gold bars, all of different weights. She gives the 24 lightest bars, which weigh 45% of the total weight, to Brennan. She gives the 13 heaviest bars, which weigh 26% of the total weight, to Maya. She gives the rest of the bars to Blair. How many bars did Blair receive?

A) 14 B) 15 C) 16 D) 17 E) 18

Discuss

Answer & Solution

Answer: Option B

Solution:

The average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya (heavy).
Let the total weight of all the bars be X.
The weight of the bars given to Brennan,
= 45% of X = 0.45X
The weight of the bars given to Maya,
= 26% of X = 0.26X
The weight of the bars given to Claire = rest = 29% of X = 0.29X
The average weight of the bars given to Brennan,
$$ = \frac{{{\text{Weight}}}}{{{\text{Number}}\,{\text{of}}\,{\text{bars}}}} = \frac{{0.45{\text{X}}}}{{24}}$$
The average weight of the bars given to Maya = Weight / number of bars = $$\frac{{0.26{\text{X}}}}{{13}}$$
Similarly, if the number of bars given to Blair = B,
then the average weight of the bars given to Blair = $$\frac{{0.29{\text{X}}}}{{\text{B}}}$$
As, the average weight of the bars given to Brennan (light) < the average weight of the bars given to Blair < the average weight of the bars given to Maya
So , Option (B) is the right answer

69

At the beginning of a year ,the owner of a jewel shop raised the price of all the jewels in his shop by x% and lowered them by x%. The price of one jewel after this up and down cycle reduced by Rs. 100. The owner carried out the same procedure after a month. After this second up-down cycle,the price of that jewel was Rs. 2304. Find the original price of that jewel(in Rs.)

A) 2500 B) 2550 C) 2600 D) 2650 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{price}} = y, \cr & {\text{After}}\,{\text{first}}\,{\text{change,}}\,{\text{it}}\,{\text{becomes}}, \cr & y \times \left( {1 + {\frac{x}{{100}}} } \right) \cr & {\text{After}}\,{\text{second}}\,{\text{change,}}\,{\text{it}}\,{\text{becomes}} \cr & y \times \left( {1 + {\frac{x}{{100}}} } \right)\left( {1 - {\frac{x}{{100}}} } \right) \cr & = y\left( {1 - {{\left( {\frac{x}{{100}}} \right)}^2}} \right) \cr & {\text{Thus}}, \cr & {x^2} \times y = {10^6} - - - - \left( 1 \right) \cr & {x^2} = \frac{{{{10}^6}}}{y} \cr & {\text{Now}}, \cr & y{\left( {1 - {\frac{{{{10}^6}}}{{10000y}}} } \right)^2} \cr & = 2304\left( {{\text{similar}}\,{\text{to}}\,{\text{above}}} \right) \cr & y{\left( {1 - \frac{{100}}{y}} \right)^2} = 2304 \cr & y = 2500 \cr} $$

70

From 2000 onwards, till 2003 the price of computers increased every year by 10%. After that due to government subsidy the price of computers decreases every year by 10%. The price of a computer in 2006 will be approx. how much per cent less than the price in 2000 if the same pattern of price is continued :

A) 2 B) 3 C) 4 D) 5

Discuss

Answer & Solution

Answer: Option B

Solution:

Year	Value
2000	100 (Let)
2001	110
2002	121
2003	133.1
2004	119.79
2005	107.811
2006	97.0299

$$\eqalign{ & {\text{Now}}, \cr & \frac{{ {\left( {100 - 97.0299} \right) \times 100} }}{{100}} \approx 3 \cr} $$