Quantitative Aptitude MCQ Quiz - Objective Question with Answer for Quantitative Aptitude - Download Free PDF

Given:

(a + b)²

Formula used:

(a + b)² = a² + 2ab + b²

Explanation:

(a + b)2 = a2 + 2ab + b2

⇒ (a + b) × (a + b)

⇒ a² + ab + ba + b²

⇒ a² + 2ab + b²

∴ (a + b)² = a² + 2ab + b²

Given:

Calculation:

⇒

⇒

⇒ 27 × 9 = 243

∴ The correct answer is: 243

Given:

Total chocolates = 60

Percentage eaten = 20%

Formula used:

Chocolates eaten = (20/100) × 60

Chocolates left = Total - Eaten

Calculation:

⇒ Chocolates eaten = (20 × 60) ÷ 100 = 1200 ÷ 100 = 12

⇒ Chocolates left = 60 - 12 = 48

∴ Ram has 48 chocolates left.

Given:

Area of rectangle = 35 cm²

Length = 7 cm

Formula used:

Area = Length × Breadth

Perimeter = 2 × (Length + Breadth)

Calculation:

⇒ 35 = 7 × Breadth

⇒ Breadth = 35 ÷ 7 = 5 cm

⇒ Perimeter = 2 × (7 + 5) = 2 × 12 = 24 cm

∴ The perimeter of the rectangle is: 24 cm

Given:

Ratio of A : B = 5 : 2

Present age of B = 18 years

Formula used:

If A : B = 5 : 2 and B = 18, then A = (5/2) × 18

Calculation:

⇒ A = (5 × 18) ÷ 2

⇒ A = 90 ÷ 2 = 45

∴ The present age of A is: 45 years

Given:

x - 1/x = 3

Concept used:

a³ - b³ = (a - b)³ + 3ab(a - b)

Calculation:

x³ - 1/x³ = (x - 1/x)³ + 3 × x × 1/x × (x - 1/x)

⇒ (x - 1/x)3 + 3(x - 1/x)

⇒ (3)³ + 3 × (3)

⇒ 27 + 9 = 36

∴ The value of x³ - 1/x³ is 36.

Alternate Method If x - 1/x = a, then x³ - 1/x³ = a³ + 3a

Here a = 3

x - 1/x³ = 3³ + 3 × 3

= 27 + 9

= 36

Given:

Profit = 25 Percent

Discount = 15 Percent

Formula:

MP/CP = (100 + Profit %)/(100 – Discount %)

MP = Printed Price

CP = Cost Price

Calculation:

We know that –

MP/CP = (100 + Profit %)/(100 – Discount %)   ………. (1)

Put all given values in equation (1) then we gets

MP/CP = (100 + 25)/(100 – 15)

⇒ 125/85

⇒ 25/17

Given:

Diameter of semicircle = 14√2 cm

Radius = 14√2/2 = 7√2 cm

Total no. of chords = 6

Concept:

Since the chords are equal in length, they will subtend equal angles at the centre. Calculate the area of one sector and subtract the area of the isosceles triangle formed by a chord and radius, then multiply the result by 6 to get the desired result.

Formula used:

Area of sector = (θ/360°) × πr²

Area of triangle = 1/2 × a × b × Sin θ

Calculation:

The angle subtended by each chord = 180°/no. of chord

⇒ 180°/6

⇒ 30°

Area of sector AOB = (30°/360°) × (22/7) × 7√2 × 7√2

⇒ (1/12) × 22 × 7 × 2

⇒ (77/3) cm²

Area of triangle AOB = 1/2 × a × b × Sin θ

⇒ 1/2 × 7√2 × 7√2 × Sin 30°

⇒ 1/2 × 7√2 × 7√2 × 1/2

⇒ 49/2 cm²

∴ Area of shaded region = 6 × (Area of sector AOB - Area of triangle AOB)

⇒ 6 × [(77/3) – (49/2)]

⇒ 6 × [(154 – 147)/6]

⇒ 7 cm²

∴ Area of shaded region is 7 cm²

Formula used

Area = length × breath

Calculation

The garden EFGH is shown in the figure. Where EF = 220 meters & EH = 70 meters.

The width of the path is 4 meters.

Now the area of the path leaving the four colored corners

= [2 × (220 × 4)] + [2 × (70 × 4)]

= (1760 + 560) square meter

= 2320 square meters

Now, the area of 4 square colored corners:

4 × (4 × 4)

{∵ Side of each square = 4 meter}

= 64 square meter

The total area of the path = the area of the path leaving the four colored corners + square colored corners

⇒ Total area of the path = 2320 + 64 = 2384 square meter

∴ Option 4 is the correct answer.

Given:

Valid votes = 75% of total votes

Winning Candidate = 70% of Valid votes

He won by a majority of 3630 votes

Losing Candidate = 30% of Valid votes

Calculation:

Let 100x be the total number of votes polled

Valid votes = 75% of total votes

= 0.75 × 100x

= 75x

Majority of the Winning Candidate is 3630

Then, Difference between Winning and Losing Candidate = (70 % - 30 %) of valid votes

= 40% of the valid votes

Valid Votes = 75x

Then,

= 0.40 × 75x

= 30x

Hence, 30x is Majority of winning candidate

30x = 3630

x = 121

Total number of votes is 100x

= 100 × 121

= 12100

Answer is 12100.

Concebt used

a.b̅ = a.bbbbbb

a.0b̅ = a.0bbbb

Calculation

0.7 = 0.700000 ̇....

Now, 0.7777…  or  is largest among all.

Given

Length of first train (L1) = 400 m

Length of second train (L2) = 300 m

Speed of second train (S2) = 60 km/hr

Time taken to cross each other (T) = 15 s

Concept:

Relative speed when two objects move in opposite directions is the sum of their speeds.

Calculations:

Let the speed of the first train = x km/hr

Total length = 300 + 400

Time = 15 sec

According to the question:

700/15 = (60 + x) × 5/18

28 × 6 = 60 + x

x = 108 km/hr.

Therefore, the speed of the longer train is 108 km per hour.

GIVEN :

If the price of petrol has increased from Rs. 40 per litre to Rs. 60 per litre

CALCULATION :

Let the consumption be 100 litres.

When price is Rs. 40 per litres, then, the expenditure = 100 × 40

⇒ Rs. 4,000.

At Rs. 60 per litre, the 60 × consumption = 4000

Consumption = 4,000/60 = 66.67 litres.

∴ Required decreased % = 100 - 66.67 = 33.33%

Given:

u : v = 4 : 7 and v : w = 9 : 7

Concept Used: In this type of question, number can be calculated by using the below formulae

Calculation:

u : v = 4 : 7 and v : w = 9 : 7

To make ratio v equal in both cases

We have to multiply the 1st ratio by 9 and 2nd ratio by 7

u : v = 9 × 4 : 9 × 7 = 36 : 63 ----(i)

v : w = 9 × 7 : 7 × 7 = 63 : 49 ----(ii)

Form (i) and (ii), we can see that the ratio v is equal in both cases

So, Equating the ratios we get,

u ∶ v ∶ w = 36 ∶ 63 ∶ 49

⇒ u ∶ w = 36 ∶ 49

When u = 72,

⇒ w = 49 × 72/36 = 98

∴ Value of w is 98

Solution:

= 25/2 + 37/3 + 73/6

= (75 + 74 + 73)/6

= 222/6

= 37

Shortcut Trick

= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)

= 36 + 1 = 37