# Quantitative Aptitude Quiz for UPSI: 12 April 2021

Updated Mon, 12 Apr 2021 04:13 PM IST

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1. If sin θ + cos θ = 1, then the value of cos 2θ is:

a) 1
b) -1
c) ±1
d) 0

Given: sin θ + cos θ = 1

Squaring both sides, we get:

⇒ sin^2 θ + cos^2 θ + 2 sin θ cos θ = 1

⇒ 1 + sin 2θ = 1

⇒ sin 2θ = 0

Using sin^2 θ + cos^2 θ = 1, we can say:

sin^2 2θ + cos^2 2θ = 1

⇒ 0 + cos^2 2θ = 1

⇒ cos 2θ = ±1.

2. If a product is sold at a 10% discount, the selling price is Rs. 72. What is the selling price of the product if the discount rate is 25%?
a)  Rs. 50
b) Rs. 64
c) Rs.

Source: Safalta

60
d) Rs. 54

Suppose marked price = Rs. x

S.P = x × (100 – 10)/100

⇒ 0.9x = 72

⇒ x = Rs. 80

On discount of 25%:

S.P = 80 × (100 – 25)/100

⇒ 80 × 0.75

⇒ Rs. 60

∴ If the discount rate is 25% then the selling price of the product is Rs. 60

3. A can complete a work in 50 days, B can complete the same work in half time of A, C can complete the same work in double the time of A, then find out the number of days taken B and C to complete the work.

a) 10
b) 15
c) 20
d) 25

B's one day work = 1/25

C's one day work = 1/100

Total work of B and C for one day = (1/25) + (1/100)

⇒ = 1/20

Total number of days for B and C = 20

4. A man goes with the average speed of 18 km/hr from Indore to Bhopal and return back to Indore with the speed of 22 km/hr. Find the average speed of man?

a)  20.8 km/hr
b)  17.8 km/hr
c)  18.8 km/hr
d)  19.8 km/hr

Average speed of man when he go from Indore to Bhopal is 18 km/hr and average speed of man when he go from Bhopal to Indore is 22 km/hr

∴ Average speed = (2 × 18 × 22/(40)) = 19.8 km/hr

∴ The average speed of man is 19.8 km/hr

5. The ratio of two numbers is 12 : 5. If each number is increased by 6 then their ratio becomes 12 : 6, then find the sum of the numbers is?

a) 34
b) 51
c) 68
d) 85

Let number is 12x and 5x

According to question,

(12x + 6) ÷ (5x + 6) = 12 ÷ 6

⇒ 72x + 36 = 60x + 72

⇒ 12x = 36

So, x = 3

Then numbers 12 × 3 = 36 and 5 × 3 = 15

Sum of the number = 36 + 15 = 51

6. The salary of A is 50% more than the salary of B. If A got a 50% rise in his salary and B got a 25% rise in his salary, then the percentage increase in their combined salaries will be:

a) 50%
b) 20%
c) 30%
d) 40%

Let the B's salary is Rs. x.

Then, A's salary = x × {(100 + 50 )/100}

⇒ x × (150/100)

⇒ 1.5x

A's new salary = 1.5x × {(100 + 50)/100}

⇒ 1.5x × {150/100}

⇒ 2.25x

B's new salary = x × {(100 + 25)/100}

⇒ x × {125/100}

⇒ 1.25x

Sum of A's old salary and B's old salary = x + 1.5x

⇒ 2.5x

Sum of A's new salary and B's new salary = 2.25x + 1.25x

3.5xPercentage increase in combined salary of A and B = {(3.5x - 2.5x)/2.5x} × 100

⇒ {1/2.5} × 100

⇒ 40%

7. The floor of a room is to be decorated with tiles of length 60 cm and width 40 cm. If dimension of floor of room is 72 m × 48 m then find the number of required tiles.

a) 16400
b) 14000
c) 14400
d) 14800

Dimension of floor = 72 m × 48 m = 7200 cm × 4800 cm

Let the number of tiles be n.

Now,

Area of total tiles = Area of floor

⇒ n × 60 × 40 = 7200 × 4800

⇒ n = (7200 × 4800)/(60 × 40)

⇒ n = 14400

8. A sum of money amounts to Rs. 4500 in 3 years and Rs. 10000 in 8 years at the same rate of simple interest. What is the principal?

a) Rs. 1600
b) Rs. 1000
c) Rs. 1200
d) Rs. 1400

S.I. for 5 years = 10000 – 4500 = Rs. 5500

⇒ SI for 1 years = 5500/5 = Rs. 1100

S I for 3 years = 3 × 1100 = Rs. 3300

Principal = 4500 – 3300 = Rs. 1200

9. Evaluate the following:

5 - [96 ÷ 4 of 3 - (16 - 55 ÷ 5)] = ?

a) 2
b) 0
c) 4
d) 1

5 - [96 ÷ 4 of 3 - (16 - 55 ÷ 5)] = ?

⇒ 5 – [96 ÷ 4 of 3 – (16 – 55/5)] = ?

⇒ 5 – [96 ÷ 4 of 3 – (16 – 11)] = ?

⇒ 5 – [96 ÷ 4 of 3 – 5] = ?

⇒ 5 – [96 ÷ 12 – 5] = ?

⇒ 5 – [96/12 – 5] = ?

⇒ 5 – [8 – 5] = ?

⇒ 5 – 3 = ?

⇒ 2 = ?

10. The ratio of the monthly income of X and Y is 5 ∶ 4 and that of their monthly expenditures is 9 ∶ 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?

a) 9 : 8
b) 8 : 9
c) 4 : 3
d) 3 : 4

Let, the income ratio of X and Y is 5a and 4a.

The expenditure ratio of X and Y is 9b and 7b.

⇒ 4a = 9b

⇒ a/b = 9/4

⇒ Saving of X = 5a - 9b

⇒ Saving of Y = 4a - 7b

⇒ Ratio = (5a - 9b)/(4a - 7b)

By dividing b

⇒ Ratio = (45 - 36)/(36 - 28)

⇒ Ratio = 9/8

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