Quantitative Aptitude PYQs

Given:

Perimeter of the rectangle = 120 cm

Ratio of length to breadth = 7 : 8

Area of the square is 4 cm² more than the area of the rectangle.

Formula used:

Perimeter of rectangle = 2 × (Length + Breadth)

Area of rectangle = Length × Breadth

Area of square = Side²

Calculations:

Let the length = 7x and the breadth = 8x (from the ratio 7:8).

Perimeter = 2 × (Length + Breadth) = 2 × (7x + 8x) = 120

⇒ 2 × 15x = 120

⇒ 30x = 120

⇒ x = 4

Length = 7x = 7 × 4 = 28 cm

Breadth = 8x = 8 × 4 = 32 cm

Area of rectangle = Length × Breadth = 28 × 32 = 896 cm²

Let the side of the square be 's'.

Area of square = s²

We are given that the area of the square is 4 cm² more than the area of the rectangle:

s² = 896 + 4

s² = 900

⇒ s = √900

⇒ s = 30 cm

∴ The side of the square is 30 cm.

Given:

Downstream distance = 64 km

Time taken for downstream = 4 hours

Upstream distance = 48 km

Time taken for upstream = 6 hours

Formula used:

Speed = Distance ÷ Time

Speed downstream = (Speed of boat + Speed of current)

Speed upstream = (Speed of boat - Speed of current)

Calculations:

Speed downstream = 64 ÷ 4 = 16 km/hr

Speed upstream = 48 ÷ 6 = 8 km/hr

Let the speed of the boat in still water be 'b' km/hr and the speed of the current be 'c' km/hr.

Speed downstream = b + c = 16

Speed upstream = b - c = 8

Now, solving the equations:

b + c = 16

b - c = 8

Add the two equations:

(b + c) + (b - c) = 16 + 8

2b = 24

b = 12 km/hr

The speed of the boat in still water is 12 km/hr.

Now, the distance covered by the boat in 5 hours in still water is:

Distance = Speed × Time

Distance = 12 × 5 = 60 km

∴ The distance covered by the boat in 5 hours in still water is 60 km.

Given:

Investment by A = Rs. x

Investment by B = Rs. (x + 5000)

Profit share ratio of A to B = 7 : 9

Formula used:

Profit share ratio = Investment ratio (since profit is directly proportional to investment)

Calculations:

Let the total profit be P.

The ratio of profit shares of A and B is given as 7:9. So, the profit for A is 7 parts and for B is 9 parts.

The total parts = 7 + 9 = 16 parts.

The profit share of A and B is directly proportional to their investments.

Investment of A / Investment of B = Profit share of A / Profit share of B

So, x / (x + 5000) = 7 / 9

Cross multiplying:

9x = 7(x + 5000)

9x = 7x + 35000

9x - 7x = 35000

2x = 35000

x = 35000 / 2 = 17500

Now, find the value of 7x:

7x = 7 × 17500 = 122500

∴ The value of 7x is Rs. 122500.

Concept used:

Calculations:

∛1331 ÷ 11 + 95 × 100 = ?

⇒ 11 ÷ 11 + 9500 = ?

⇒ 1 + 9500 = ?

⇒ 9501 = ?

∴ The value of ? is 9501.

Concept:

Follow BODMAS rule to solve this question, as per the order given below, 

Calulations:

Given expression is

53 ÷ 57 × 252 of 12 − 125% of 8 = ?

⇒ 53 ÷ 57 × 54 × 12 − 125% of 8 = ?

⇒ (53 / 57) × 54 × 12 − 125% of 8 = ?

⇒ (1 / 54) × 54 × 12 − 125% of 8 = ?

⇒ \( {1 \over 25^2}\) × 25² × 12 - 10 = ?

⇒ 1 × 12 - 10 = ?

∴ ? = 2

Given:

(7/132) × (528/9) × √64 ÷ (2/9)

Concept used:

We have to follow the BODMAS rule

Calculation:

7 × (4/9) × 8 ÷ (2/9) = ?

⇒ 7 × (4/9) × 8 × (9/2) = ?

⇒ (28/9) × 36 = ?

⇒ ? = 28 × 4 = 112

∴ The value of ? is 112.

Concept Used: 

Follow the BODMAS rule according to the table given below:

Calculation:

18 + 12 × 6 - 12 ÷ 3 + 77 ÷ 11 = ?

⇒ 18 + 72 - 4 + 7 = ?

⇒ 18 + 79 - 4 = ?

⇒ ? = 97 - 4

∴ 93 will come in place of the question mark ('?').

Concept used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

1.6% of 1000 × 2.4% of ? = 288

⇒ 16 × (2.4/100) of ? = 288

⇒ ? = (288 × 100)/(2.4 × 16)

⇒ ? = 750

∴ The value of ? is 750

Concept used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

12.5% of 32 + 32.5% of 280 = 92 + (?)

12.5% = 1/8, 

32.5% = 20% + 12.5% = (1/5) + (1/8) = 13/40

Putting the values,

(32/8) + (280/40) × 13 = 81 + (?)

4 + 91 = 81 + (?)

? = 95 - 81 = 14

∴ ? = 14

Alternate Method Fraction value of 12.5% = 1/8

Fraction value of  32.5% = 13/40

12.5% of 32 + 32.5% of 280 = 92 + (?)

⇒ (1/8 × 32) + (13/40 × 280) = 81 + ?

⇒ 4 + 91 = 81 + ?

⇒ 95 = 81 +  ?

⇒ ? = 95 - 81 = 14

Given:

\(56\frac{1}{2}% ;{\rm{of; }}1400{\rm{;}} - {\rm{;}}? = 230\)

Concept used:

We have to follow the BODMAS rule

Calculation:

113/200 of 1400 – ? = 230

⇒ 791 – ? = 230

⇒ ? = 791 – 230 = 561

∴ The value of ? is 561.

Given:

(1/19)(7 × 9 – 12 × 4 + 46 ÷ 2)

Concept used:

We have to follow the BODMAS rule

Calculation:

(1/19)(63 – 48 + 23) = ?

⇒ (1/19)(86 – 48) = ?

⇒ (1/19)(38) = ?

⇒ ? = 2

∴ The value of ? is 2.

Concept:

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated. 

Calculation:

Given expression is 

(30% of 230 + 10% of 130) = ? + 34

⇒(69 + 13) = ? + 34 

 ⇒ (82) = ? + 34 

⇒ 82 - 34 = ?

∴ ? = 48

Calculation:

We use the BODMAS rule as follows:

According to the rule ‘Bracket’ should be solved first

⇒ ?% of (19154 - 15644) = 9² + 6²

⇒ ?% of 3510 = 81 + 36

⇒ (?/100) × 3510 = 117

⇒ ? = (117/351) × 10

⇒ ? = 10/3

∴ Required answer is 10/3.

Given:

66.66% of 480 + 37.5% of 832 = 120 + ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

66.66% of 480 + 37.5% of 832 = 120 + ?

⇒ 2/3 × 480 + 3/8 × 832 = 120 + ?

⇒ 320 + 312 = 120 + ?

⇒ ? = 512

∴ The value of ? is 512.

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is

15% of 440 = 25% of ? + 20% of 280

⇒ 66 = 25% of ? + 56

⇒ 10 = 25% of ?

⇒ 10 × 4 = ?

⇒ 40 = ?

⇒ ? = 40

∴ ? = 40

Concept used:

Calculation:

\(4\frac{1}{3} + 2\frac{7}{4} - 5\frac{{11}}{3} = ? + 2\frac{4}{3}\)

⇒ \(4\frac{1}{3} + 2\frac{7}{4} - 5\frac{{11}}{{3}} - 2\frac{4}{3} = ;?\)

⇒ ? = (4 + 2 – 5 – 2) + \(\frac{1}{3} + \frac{7}{4} - \frac{{11}}{3} - \frac{4}{3}\)

⇒ ? = - 1 + \(\frac{{4 + 21 - 44 - 16}}{{12}}\)

⇒ ? = - 1 + (-\(\frac{{35}}{{12}}\))

⇒ ? = -1 - \(\frac{{35}}{{12}}\)

⇒ \(? = ; - \frac{{47}}{{12}} = ; - 3\frac{{11}}{{12}}\)

⇒ Hence, \(; - 3\frac{{11}}{{12}}\) is the correct answer.

Concept Used:

We have to follow the BODMAS rule,

Calculation:

(36 × 15) - 40% of (20)² = ?

⇒ 540 - 40/100 × 400 = ?

⇒ 540 - 160 = ?

⇒ 380 = ?

∴ The value of ? is 380.

Concept Used:

We have to follow the BODMAS rule

Calculation:

25% of 8284 - 18% of 1500 = ?

⇒ 25/100 × 8284 - 18/100 × 1500 = ?

⇒ 2071 - 270 = ?

⇒ ? = 1801

∴ The value of ? is 1801.

Given:

Total sum = Rs. 4350

A receives 25% more than C

B receives 20% more than A

Formula used:

Let the amount received by C = x

Amount received by A = x + 25% of x = 1.25x

Amount received by B = 1.25x + 20% of 1.25x = 1.25x + 0.25x = 1.5x

Calculations:

Total amount = x + 1.25x + 1.5x = 4350

3.75x = 4350

x = 4350 / 3.75

x = 1160

Amount received by B = 1.5x = 1.5 × 1160 = 1740

∴ The amount received by B is Rs. 1740.

Given:

Distance covered by first bus = 320 km

Time taken by first bus = 8 hours

Speed of second bus = 25% more than first bus

Distance to be covered by second bus = 200 km

Formula used:

Speed = Distance / Time

Calculations:

Speed of first bus = 320 km / 8 hours = 40 km/h

Speed of second bus = 40 km/h + 25% of 40 km/h = 40 km/h + 10 km/h = 50 km/h

Time taken by second bus to cover 200 km = Distance / Speed

Time = 200 km / 50 km/h = 4 hours

∴ The time taken by the second bus to cover 200 km is 4 hours.