Mock Test: Numerical Ability - 7 - AFCAT MCQ

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

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

5aⁿ =aⁿ .a
a=5

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

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

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

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.

2/3*π*8³ = n*4*2/3*π*2³
n = 16

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

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

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

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

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

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