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Mock Test: Numerical Ability - 7 - AFCAT MCQ


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15 Questions MCQ Test - Mock Test: Numerical Ability - 7

Mock Test: Numerical Ability - 7 for AFCAT 2024 is part of AFCAT preparation. The Mock Test: Numerical Ability - 7 questions and answers have been prepared according to the AFCAT exam syllabus.The Mock Test: Numerical Ability - 7 MCQs are made for AFCAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mock Test: Numerical Ability - 7 below.
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Mock Test: Numerical Ability - 7 - Question 1

When one-fourth of a number is added to 16, it becomes three-fourth of itself. Find the number?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 1

a/4 + 16 = 3a/4,
2a/4 = 16, so a = 32

Mock Test: Numerical Ability - 7 - Question 2

What is the angle between the hands at 4.40?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 2

Angle between hands of a clock 

When the minute hand is behind the hour hand, the angle between the two hands at MM minutes past HH 'o clock

When the minute hand is ahead of the hour hand, the angle between the two hands at MM minutes past HH 'o clock

Here H = 4, M = 40 the minute hand is ahead of the hour hand. Hence the angle

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Mock Test: Numerical Ability - 7 - Question 3

Direction (Q. 19-20). Each question below is followed by statements I and II. You have to determine whether thedata given in the statement is sufficient for answering the questions or not.

Q.

an + an + an + an + an + an = an+1 then what is the value of n?
I. an = 255
II. a = 5

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 3

5an =an .a
a=5

Mock Test: Numerical Ability - 7 - Question 4

A motor car does a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey.

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 4

If the car does half the journey @ 30 kmph and the other half at 40 kmph it’s average speed can be
estimated using weighted averages.
Since, the distance traveled in each part of the journey is equal, the ratio of time for which the car
would travel would be inverse to the ratio of speeds. Since, the speed ratio is 3:4, the time ratio
for the two halves of the journey would be 4:3. The average speed of the car would be:
(30 × 4 + 40 × 3)/7 = 240/7 kmph.
It is further known that the car traveled for 17.5 hours (which is also equal to 35/2 hours).
Thus, total distance = average speed × total time = (240 × 35)/(2 × 7) = 120 × 5 = 600 km

Mock Test: Numerical Ability - 7 - Question 5

A father left a will of Rs.5 lakhs between his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.5 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 5

Answer – A.Rs.2,04,797 Explanation : Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (5,00,000 – x).
The elder daughter’s money earns interest for (21 – 15) = 6 years @ 10% p.a simple interest The younger daughter’s money earns interest for (21 – 10) = 11 years @ 10% p.a simple interest.
As the sum of money that each of the daughters get when they are 21 is the same, x + (6*10*x/100)= (5,00,000 – x) +(11*10*[5,00,000-x]/100) 100x+60x = (5,00,000-x)+(55,000,000-110x) 160x =55,500,000-111x 271x = 55,500,000 X = 2,04,797

Mock Test: Numerical Ability - 7 - Question 6

Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 6

Let present age of P and Q be 3x
and  4x  respectively.
Ten years ago, P was half of Q's age

Total of their present ages
=3x+4x=7x=7×5=35

Mock Test: Numerical Ability - 7 - Question 7

Two taps are running continuously to fill a tank. The 1st tap could have filled it in 5 hours by itself and the second one by itself could have filled it in 20 hours. But the operator failed to realise that there was a leak in the tank from the beginning which caused a delay of one hour in the filling of the tank. Find the time in which the leak would empty a filled tank.

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 7

Without the leak:
Rate of work = 20% + 5% = 25%. Thus, it would have taken 4 hours to complete the work.
Due to the leak the filling gets delayed by 1 hour. Thus, the tank gets filled in 5 hours. This means
that the effective rate of filling would be 20% per hour. This means that the rate at which the leak
empties the tank is 5% per hour and hence it would have taken 20 hours to empty a filled tank.

Mock Test: Numerical Ability - 7 - Question 8

A hemispherical bowl of diameter 16cm is full of ice cream. Each student in a class is served exactly 4 scoops of ice cream. If the hemispherical scoop is having a radius of 2cm, then ice cream is served to how many students?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 8

2/3*π*8³ = n*4*2/3*π*2³
n = 16

Mock Test: Numerical Ability - 7 - Question 9

If a man spends 1000rs for the first five months, 2000rs for the next four months and 3000rs for the next 3 months and he saves 2000rs in the whole year then his average monthly salary will be ?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 9

Answer – b) 2000 Explanation : 1000*5 + 2000*4 + 3000*3 + 2000 = 24000
24000/12 = 2000

Mock Test: Numerical Ability - 7 - Question 10

What should come in place of the question mark '?' in the following number series?
10, 5, ?, 10, 40, 320

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 10

The given number series follows the pattern:

10 × 2-1 = 5

5 × 20 = 5

5 × 21 = 10

10 × 22 = 40

40 × 23 = 320

 The number coming in place of “?” in the given number series is 5

Mock Test: Numerical Ability - 7 - Question 11

What is the difference between compound interest and simple interest for the sum of Rs. 20,000 over a 2 year period if the compound interest is calculated at 20% and simple interest is calculated at 23%?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 11

Mock Test: Numerical Ability - 7 - Question 12

A bag contains 6 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 12

(8c1)/(14c1) * (8c1)*(14c1) = 16/49

Mock Test: Numerical Ability - 7 - Question 13

If a = -2 and b = -5 then find the value of a3 + b3– a2 + b2 + 2a – 3b

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 13

a3 + b3– a2 + b2 + 2a – 3b
(-2)3 + (-5)3 – (-2)2 + (-5)2 + 2(-2) – 3(-5) = -8 -125-4+25-4+15 = -101

Mock Test: Numerical Ability - 7 - Question 14

A and B can do a piece of work in 20 and 25 days respectively. They began to work together but A leaves after some days and B completed the remaining work in 12 days. Number of days after which A left the job

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 14

(1/20 + 1/25)*T + 12/25 = 1
We will get T = 52/9  days

Mock Test: Numerical Ability - 7 - Question 15

 An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

Detailed Solution for Mock Test: Numerical Ability - 7 - Question 15

Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)

= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m

Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40

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