Quant Quiz

Directions (1-4): What approximate value should come in the place of question mark (?) in the following questions?

Q1. 6245.998 ÷ 18.01 × 39.88 = ? ÷ 25.089 × 40.01

(a) 8675 

(b) 8275 

(c) 9675 

(d) 8075 

(e) 7975

Q2. 19.85% of 1540 + 13.899% of 1050 = 20% of ?

(a) 3175 

(b) 2975 

(c) 1875 

(d) 2275 

(e) 1675

Q3. 958.08 × 779.98 ÷ 24.01 = ?

(a) 30067.5 

(b) 3942.5 

(c) 30098.5 

(d) 31342.5 

(e) 31135

Q4. 377.98 ÷ 8.93 + 123.94 ÷ 8.01 + 1460 × 1.25 = ?

(a) 2945.5 

(b) 2872.5 

(c) 2882.5 

(d) 1882.5 

(e) 2688.5

Q5. In a regular week, there are 6 working days for each day the working hours are seven. A man gets Rs. 80 per hour for regular work and Rs. 100 per hour for over time. If he earns Rs. 30,880 in 8 weeks, then for how many hours does he work?

(a) 330 hours 

(b) 376 hours 

(c) 296 hours 

(d) 384 hours 

(e) 288 hours

Q6. Two men together start a journey in the same direction. They travel 24 and 36 km per day respectively. After travelling of 6 days the man at 24 km per day doubles his speed and both of them finish the journey in the same time. Find the number of days taken by them to reach the destination.

(a) 10 days 

(b) 6 days 

(c) 8 days 

(d) 14 days 

(e) 12 days

Q7. The income of Roshan and Surbhi are in the ratio 9 : 4 and their ratio of expenditure is 7 : 3. If each saves Rs. 5000, what is the sum of their expenditure?

(a) Rs. 215000 

(b) Rs. 225000 

(c) Rs. 250000 

(d) Rs. 245000 

(e) Rs. 275000

Q8. P, Q and R invest in a business. If the ratio of their time period are 3 : 4 : 5 and their profits are in the ratio 5 : 6 : 8. Find the ratio in which the investment are made by P, Q and R.

(a) 50 : 45 : 48 

(b) 51 : 45 : 47 

(c) 51 : 46 : 48 

(d) 50 : 45 : 47 

(e) 50 : 47 : 48

Q9. If the price of commodity be raised by 18 (2/3) %, find by how much percent must a householder reduce his consumption of that commodity, so as not to increase his expenditure?

(a) 14% 

(b) 15.73% 

(c) 12% 

(d) 13.25% 

(e) 16.43%

Q10. Ten years ago, Anushka was thrice as old as Abhishek was, but 14 years hence, Anushka will be only twice as old as Abhishek. Find the present age of Anushka.

(a) 72 years 

(b) 80 years 

(c) 78 years 

(d) 76 years 

(e) 82 years

Directions (11-15): In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. 

Q11. 

I. 12x² – 59x + 72 = 0

II. 8y² – 58y + 99 = 0

(a) if x > y 

(b) if x >= y 

(c) if x < y

(d) if x <= y 

(e) if x = y or relationship between x and y cannot be determined.

Q12. 

I. x² + x – 20 = 0

II. y² + 13y + 40 = 0

(a) if x > y 

(b) if x >= y 

(c) if x < y

(d) if x <= y 

(e) if x = y or relationship between x and y cannot be determined.

Q13. 

I. x² + 12x + 36 = 0

II. 5y² – 2 √15y + 3 = 0

(a) if x > y 

(b) if x >= y 

(c) if x < y

(d) if x <= y 

(e) if x = y or relationship between x and y cannot be determined.

Q14. 

I. 10x² – 29x – 21 = 0

II. y² + 13y – 68 = 0

(a) if x > y 

(b) if x >= y 

(c) if x < y

(d) if x <= y 

(e) if x = y or relationship between x and y cannot be determined.

Q15. 

I. 72x² – 163x + 88 = 0

II. 56y² – 187y + 156 = 0

(a) if x > y 

(b) if x >= y 

(c) if x < y

(d) if x <= y 

(e) if x = y or relationship between x and y cannot be determined.

Solutions

S1. Ans.(a)

Sol. 6246/18 * 40 = ? / 25 * 40

? = 8675

S2. Ans.(d)

Sol. 20% * 1540 + 14% * 1050 = 20% * ?

? = (308 + 147)/0.2

? = 2275

S3. Ans.(e)

Sol. 958 * 780 / 24 = 31135

S4. Ans.(d)

Sol. 378/9 + 124/8 + 1460*1.25 = 42 + 15.5 + 1825 = 1882.5

S5. Ans.(b)

Sol. Let the man works overtime for x hours

Now, working hours in 8 weeks

= 8 × 6 × 7 = 336 hours

336 × 80 + x × 100 = 30880

100x = 30880 – 26880 = 4000

x = 40

Total hours = 336 + 40 = 376 hours

S6. Ans.(e)

Sol. Distance travelled by 1st man in 6 days

D1 = 24 × 6 = 144 km

and by 2nd man

D2 = 36 × 6 = 216 km

Let the total distance be x km

For remaining distance, let both take t days to reach the final destination

x – 144 = 2 × 24 t

x – 144 = 48 t -- (i)

and x – 216 = 36 t -- (ii)

from (i) and (ii), we get

Then, x – 144 – x + 216 = 48t – 36t

72 = 12 t

t = 6 days

Total days = 6 + 6 = 12 days

S7. Ans.(c)

Sol. Roshan’s saving = 

9x – 7y = 5000

Surbhi’s savings = 

4x – 3y = 5000

So, y = 25000

Total expenditure = 7y + 3y = 10y = 10 * 25000 = Rs. 250000

S8. Ans.(a)

Sol. Ratio of their investment

= 5/3 : 6/4 : 8/5

= 5/3 : 3/2 : 8/5

= 50 : 45 : 48

S9. Ans.(b)

Sol. Required reduction in consumption

= 56/3 * 1/(100 + 56/3) * 100

= 56/3 * 3/356 * 100 = 15.73%

S10. Ans.(e)

Sol. Let the age of Anushka = x and Abhishek = y

(x-10) = 3(y-10)

And, (x+14) = 2(y+14)

Y = 34, x = 82

S11. Ans.(c)

Sol. I. 12x² – 32x – 27x + 72 = 0

(3x – 8) (4x – 9) = 0

x = 8/3, 9/4

II. 8y² – 22y – 36y + 99 = 0

(2y – 9) (4y – 11) = 0

y = 9/2, 11/4

x < y

S12. Ans.(b)

Sol. I. x² + 5x – 4x – 20 = 0

(x – 4) (x + 5) = 0

x = 4, –5

II. y² + 5y + 8y + 40 = 0

(y + 8) (y + 5) = 0

y = –8, – 5

x >= y

S13. Ans.(c)

Sol. I. (x + 6)² = 0

x = –6

II. 2

(√ 5y – √ 3)² = 0

y = √ 3/ √ 5

x < y

S14. Ans.(e)

Sol. I. 10x² – 35x + 6x – 21 = 0

(5x + 3) (2x – 7) = 0

x = –3/5, 7/2

II. y² + 17y – 4y – 68 = 0

(y – 4) (y + 17) = 0

y = 4, – 17

No relationship between x and y exists.

S15. Ans.(c)

Sol. I. 72x² – 64x – 99x + 88 = 0

(8x – 11) (9x – 8) = 0

x = 11/8, 8/9

II. 56y² – 91y – 96y + 156 = 0

(7y – 12) (8y – 13) = 0

y = 12/7, 13/8

x < y