Mock Test: Numerical Ability - 10 - AFCAT MCQ

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

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


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

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:

⇒ 28x - 9,600 = 24x - 4,800
⇒ 4x = 4,800
⇒ x = 1,200
Monthly income of Ravi = 8x = (8 × 1,200) = Rs. 9,600

 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

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

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.

Volume of a sphere

Surface area = 4πr² 

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

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.

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

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.

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

= 3.6 km

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 

► 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

Going through the options, 8181/1818 = 4.5

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