Quant Quiz

Q1. Bhavika alone would take 8 h more to complete the job than when Bhavika and Rita worked together. If Rita worked alone, she would take 4½ hrs more to complete the job than when Bhavika and Rita worked together. What time would they take if both Bhavika and Rita worked together ?
(1) 5 days 
(2) 4 days
(3) 3 days 
(4) 6 days
(5) None of these

Q2. If 36 men can dig a trench 200 m long, 3 m wide and 2 m deep in 6 days working 10 h a day, in how many days, working 8 h a day will 10 men dig a trench 100 m long, 4 m wide and 3 m deep ?
(1) 15 days
(2) 27 days
(3) 20 days
(4) 54 days
(5) None of these

Q3. A train can travel 20% faster than a car. Both start from the point A at the same time and reach point B, 75 km away from A at the same time. On the way however the train lost about 12.5 min while stopping at the stations. The speed of the car is
(1) 50 km/h 
(2) 55 km/h
(3) 60 km/h 
(4) 65 km/h
(5) None of these

Q4. Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes the slower train in 36 s. The length of each train is
(1) 50 m 
(2) 80 m
(3) 72 m 
(4) 82 m
(5) None of these

Q5. An automobile financier claims to be lending money at simple interest but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes
(1) 10% 
(2) 10.25%
(3) 10.5% 
(4) 10.35%
(5) None of these

Directions (Q6 – Q10): In each of these questions a number series is given. In each series only one number is wrong. Find out that number.

Q6. 2 12 36 81 150 252
(1) 2 
(2) 81 
(3) 36 
(4) 150 
(5) 252

Q7. 5 16 27 44 65 90
(1) 16 
(2) 5 
(3) 44 
(4) 65 
(5) 90

Q8. 4 2 0 -5 -12 -21
(1) 0 
(2) 4 
(3) 2 
(4) -5 
(5) -21

Q9. 101 123 149 179 218 251
(1) 251 
(2) 123 
(3) 179 
(4) 218 
(5) 101

Q10. 9 21 45 101 211 433 879
(1) 21 
(2) 45 
(3) 211 
(4) 433 
(5) 101

Answers:

Q1 – (4)
Let Bhavika and Rita working together
can finish a job in x days.
Then, in 1 day they will complete = 1/x work
Bhavika working alone do in 1 day = 1/(x+8) work
Rita working alone will do in 1 day = 1/(x+9/2) work
So, 1/(x+8) + 1/(2x+9) = 1/x
=> [(2x+9) + 2(x+8)]/[(x+8)(2x+9)] = 1/x
=> x = 6days

Q2 – (2)
According to Question 
M1 x D1 x T1 x W2 = M2 x D2 x T2 x W1
36 x 6 x 10 x 1200 = 10 x D2 x 8 x 1200
D2 = 36 x 6 x 10 x 1200 / 10 x 9 x 1200 = 27days

Q3 – (3)
Let the speed of the car be x km/h
So, Speed of train = x * 1.2x = 6x / 5 km/h
So, 5/6x * 75 + 25/(2*60) = 75/x
= 75*2*60/6*25 = 60km/h

Q4 – (1)
Let the length of each train be x mtr
Then, total distance covered = (x + x) = 2x mtr
Relative Speed = (46 – 6) = 10 km/h = 10*5/18 m/s
Given (time) 36 = 2x * 18/50

Q5 – (2)
According to question, S.I. on Rs. 100 at 10% for six months 
=(100*10*6)/(100*12) = Rs. 5
Principal for next six months = Rs. 105
SI = 105*10*6/100*12 = Rs. 5.25
Total interest = Rs. 10.25

Q6 – (2)
The series is 1² x 2 = 2, 2² x 3 = 12, 3² x 4 = 36, 4² x 5 = 80 and so on.. Hence, 81 should be replaced by 80.

Q7 – (1)
The series is 1 x (2+3) = 5, 2 x (3+4) = 14, 3 x (4+5) = 27 and so on..
Hence, 16 should be replaced by 14

Q8 – (3) 
The series is 3² – 2² – 1² = 4, 4² – 3² – 2² = 3 and so on..
Hence, 2 should be replaced by 3.

Q9 – (4)
The series is 10² + ² + 0² = 101, 11² + 1² + 1² = 123, 12² + 1² + 2² = 149 and so on..
Hence, 218 should be replaced by 213

Q10 = (2)
The series is x 2 + 3, x 2 + 5, x 2 + 7, x 2 + 9, x2 + 11 and so on..
Hence, 45 should be replaced by 47.