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AFCAT Exam  >  AFCAT Tests  >  Mock Test: Numerical Ability - 10 - AFCAT MCQ

Mock Test: Numerical Ability - 10 - AFCAT MCQ


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15 Questions MCQ Test - Mock Test: Numerical Ability - 10

Mock Test: Numerical Ability - 10 for AFCAT 2024 is part of AFCAT preparation. The Mock Test: Numerical Ability - 10 questions and answers have been prepared according to the AFCAT exam syllabus.The Mock Test: Numerical Ability - 10 MCQs are made for AFCAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mock Test: Numerical Ability - 10 below.
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Mock Test: Numerical Ability - 10 - Question 1
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If N = (11111111)2, then what is the sum of the digits of N?

Detailed Solution for Mock Test: Numerical Ability - 10 - Question 1

12 = 1, 112 = 121, 1112 = 12321, 11112 = 1234321 and 111112 = 123454321
⇒ 111111112 = 123456787654321
The sum of the digits of given number is 64.

Mock Test: Numerical Ability - 10 - Question 2
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The monthly income of a person was Rs. 1350 and his monthly expenses were Rs. 900. Next year, his income increased by 14% and expenses decreased by 7% only. Find the percentage increase in the savings.  

Detailed Solution for Mock Test: Numerical Ability - 10 - Question 2

Old savings = Rs. (1350 - 900) = Rs. 450


New savings = Rs. (1539 - 837) = Rs. 702
%age of increased savings 

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Mock Test: Numerical Ability - 10 - Question 3
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The monthly incomes of Vasu and Ravi are in the ratio 7 : 8 and their monthly expenditures are in the ratio 3 : 4, respectively. If the respective savings of Vasu and Ravi are Rs. 2,400 and Rs. 1,600, then find the monthly income of Ravi.

Detailed Solution for Mock Test: Numerical Ability - 10 - Question 3

Ratio of monthly incomes of Vasu and Ravi = 7 : 8
Let their incomes be 7x and 8x, respectively.
Ratio of their expenditures = 3 : 4
Expenditure = Income - Savings
Savings of Vasu = Rs. 2,400
His expenditure = (7x - 2,400)
Savings of Ravi = Rs. 1,600
His expenditure = (8x - 1,600)
According to question:
$\small \frac{(7x-2400)}{(8x-1600)} = \small \frac{3}{4}$
⇒ 28x - 9,600 = 24x - 4,800
⇒ 4x = 4,800
⇒ x = 1,200
Monthly income of Ravi = 8x = (8 × 1,200) = Rs. 9,600

Mock Test: Numerical Ability - 10 - Question 4
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A father left a will that his capital of Rs. 18,750 should be divided between his two sons aged 12 years and 14 years, respectively, when they attain maturity at the age of 18 years. The amount received by each at 5% simple interest would be the same. Find the sum allotted to the elder son.
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 4

 Let the amount be Rs. x and Rs. y for the younger and elder son, respectively.
x + y = Rs. 18,750 ... (I)
Applying simple interest :
 x (1 + 6 × 5/100) = y (1 + 4 × 5/100) [ We know: S.I = (P×R×T)/100]
 x/12 = y/13 = 750
 x = Rs. 9,000
y = Rs. 9,750
Hence, amount allotted to elder son = Rs. 9,750

Mock Test: Numerical Ability - 10 - Question 5
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Mr. Khanna pays 10% pa interest on an amount borrowed and lends this amount at 12% pa. If at the end of the year, he earns Rs. 2.4 crore as simple interest in the transaction, then what is the sum transacted?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 5

Net rate = 2%
SI at 2% of money transacted = 
x = 120 crore

Mock Test: Numerical Ability - 10 - Question 6
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The price of wheat is reduced by 4%. How many more or less kg of wheat can now be bought for the money which was sufficient to buy 48 kg wheat earlier?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 6

Given:

The price of wheat is reduced by 4%.

Assumption:

Let the price of wheat be Rs.100/kg.

Calculation:

The price of 48 kg wheat  = 4800

As price is reduce by 4% it means that it became 96% of initial 100% hence,

After price decrease = 4800/96 = 50 kg

Hence, the required quantity of wheat = (50 – 48) = 2 kg more.

Mock Test: Numerical Ability - 10 - Question 7
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The ratio of the volume of a sphere to its surface area is  
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 7

Volume of a sphere

Surface area = 4πr2 

Ratio of the volume to the surface area = r : 3

Mock Test: Numerical Ability - 10 - Question 8
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Three groups of children contain 3 girls and 1 boy, 2 girls and 2 boys, and 1 girl and 2 boys respectively. One child is selected at random from each group. The probability that the three selected consist of 1 girl and 2 boys is
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 8

Girl and Boy and Boy or Boy and Girl and Boy Or Boy and Boy and Girl
= (3/4) X(2/4) X(2/3) + (1/4) X(2/4) X(2/3) + (1/4) X(2/4) X(1/3) = 18/48 = 3/8.

Mock Test: Numerical Ability - 10 - Question 9
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The dimensions of a field are 20 m by 9 m. A pit 10 m long, 4.5 m wide and 3 m deep is dug in one corner of the field and the earth removed is evenly spread over the remaining area of the field. What will be the rise in the height of the field as a result of this operation?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 9

Volume of the earth removed = Area of remaining field × Rise in Height
⇒10 × 4.5 × 3 = (180 – 45) × h
135/135 = h
⇒ h = 1

Mock Test: Numerical Ability - 10 - Question 10
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In the beginning of 2020, the population of three cities 'A', 'B', and 'C' was in the ratio of 4 : 5 : 6 respectively. During the year 2021, the population of respective cities increased by a percentage in the ratio of 7 : 5 : 9. In the beginning of 2021, the population of city 'C' was 27000 more than that of the beginning of the year 2020 and in the beginning of the year 2021 the ratio of the population of A : B was 108 : 125 then during the year 2020, what was the sum of the increase in the population of all the cities together?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 10

Given:

Population of A : B : C = 4 : 5 : 6 (in the beginning of 2020)

Percentage increase in the population of A : B : C = 7 : 5 : 9

Population of city 'C' (in 2021) - Population of city 'C' (in 2020) = 27000

Population of A : B (in the beginning of 2021) = 108 : 125

Calculation:

Let the population of city 'A', 'B' and 'C' was 7x, 5x and 9x (in the beginning of 2020)

And the percentage increase in the population of cities = 7y%, 5y%, and 9y%.

ATQ, 6x × [(100 + 9y)/100] - 6x = 27000 ...(i)

Again (4x) × [(100 + 7y)/100]/(5x) × [(100 + 5y)/100] = 108/125

⇒ (100 + 7y)/(100 + 5y) = 27/25

⇒ 40y = 200

⇒ y = 5

Using (i)

⇒ 6x × 145% - 6x = 27000

⇒ x = 10000

Population of city A (in 2020) = 4x = 40000

Population of city B (in 2020) = 5x = 50000

Population of city C (in 2020) = 6x = 60000

The sum of the increase in the population of all the cities together = 35% × 40000 + 25% × 50000 + 45% × 60000 = 53500

Hence, the correct answer is 53500.

Mock Test: Numerical Ability - 10 - Question 11
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The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 11

Speed downstream
= (15 + 3) kmph
= 18 kmph
Distance travelled

= 3.6 km

Mock Test: Numerical Ability - 10 - Question 12
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Two balls are drawn at random from a bag containing 3 white, 3 red, 4 green and 4 black balls one by one without replacement. Find the probability that both the balls are of different colours.
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 12

Probability that the 1st ball is white and the 2nd ball is other than white =

Probability that the 1st ball is red and the 2nd ball is other than red 

Probability that the 1st ball is green and the 2nd ball is other than green

Probability that the 1st ball is black and the 2nd ball is other than black 

Probability that both the balls are of different colours 

Mock Test: Numerical Ability - 10 - Question 13
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Shalaj and Associates, a shoe-manufacturing company, has three machines producing shoes. If machine X produces l/4th as many as machine Y produces in the same time, and machine Y produces twice as many as machine Z produces in the same time, then during a fixed time, what fraction of the total number of shoes is produced by machine Z?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 13

► Assume that Y produces 4P units in unit time.
► Then X and Z produce P and 2P units in the same time.
► So, Total shoes produced = 7P, Fraction of the total number of shoes produced by machine Z = 2/7

Mock Test: Numerical Ability - 10 - Question 14
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The History teacher was referring to a year in the 19th century. Rohan found an easy way to remember the year. He found that the number, when viewed in a mirror, increased 4.5 times. Which year was the teacher referring to?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 14

Going through the options, 8181/1818 = 4.5

Mock Test: Numerical Ability - 10 - Question 15
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A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Detailed Solution for Mock Test: Numerical Ability - 10 - Question 15

C's 1 day's work = 1/3 - (1/6 + 1/8)
⇒ 1/3 - 7/24
⇒ 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24
⇒ 4 : 3 : 1
C's share (for 3 days) = Rs.(3 * 1/24 * 3200)
⇒ Rs. 400

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