Quant Quiz

Directions (Q. Nos. 1 to 4): Read the following and answer the questions that follow:
Two friends Shyam and Kailash own two versions of a car. Shyam owns the diesel version while Kailash owns petrol version. Kailash’s car gives an average that is 20%  higher than Shyam’s (in terms of litres per kilometre). It is known that petrol costs 60% of its price higher than diesel.

1. The ratio of cost per kilometre of Kailash’s car to Shyam’s car is:
(A) 3 : 1
(B) 1 : 3
(C) 1.92 : 1
(D) cannot be determined
(E) None of these

2. Shyam’s car gives an average of 20 km per litre, then the difference in the cost of travel per kilometre between the two cars is:
(A) Rs 4.3
(B) Rs 3.5
(C) Rs 2.5
(D) cannot be determined
(E) None of these

3. For the above question (26), the ratio of the costs per kilometre of the Shyam’s travel to Kailash’s travel is:
(A) 3 : 1
(B) 1 : 3
(C) 1 : 1.92
(D) cannot be determined
(E) None of these

4. Diesel costs Rs 12.5 per litre, then the difference in the cost of travel per kilometre between Kailash’s and Shyam’s is (assume an average of 20 km per litre for  Shyam’s car and also assume that petrol is 50% of its own price higher than diesel):
(A) Rs 1.75
(B) Rs 0.875
(C) Rs 1.25
(D) Can not be determined
(E) None of these

5. A shopkeeper gives 3 consecutive discounts of 10%, 15% and 15% after which he sells his goods at a percentage profit of 30.05% on the cost price. Find the value of  the percentage profit that the shopkeeper would have earned if he had given discounts of 10% and 15% only:
(A) 53%
(B) 62.5%
(C) 72.5%
(D) 68.6%
(E) None of these

6. A journey of 192 kms takes 2 hours less by a fast train than by a slow train. If the average speed of the slow train is 16 kmph less than that of a fast train, what  is the average speed of the fast train?
(A) 30 kmph
(B) 48 kmph
(C) 20 kmph
(D) 25 kmph
(E) None of these

7. Two planes move along a circle of circumference 1.2 kms with constant speeds. When they move in different directions, they meet every 15 seconds and when they move in the same direction one plane overtakes the other every 60 seconds. Find the speed of the slower plane:
(A) 0.04 km/s
(B) 0.03 km/s
(C) 0.05 km/s
(D) 0.02 km/s
(E) None of these

8. The metro service has a train going from Mumbai to Pune and Pune to Mumbai every hour. The first one at 6 a.m. The trip from one city to another takes 4.5 hours,  and all trains travel at the same speed. How many trains will pass while going from Mumbai to Pune, if you start at 12 noon?
(A) 8
(B) 10
(C) 13
(D) 9
(E) None of these

9. A bus left Delhi for Ambala at 50 km/hr and turned over the same route at 40 km/hr. Thus it took 1 hour more on the return trip. The distance between Delhi and  Ambala is:
(A) 200 kms
(B) 180 kms
(C) 400 kms
(D) 300 kms
(E) None of these

10. A man purchased a bag of rice containing 70 kgs for Rs 175. He sold it at the rate of Rs 2.75 per kg. Find the profit and loss per cent.
(A) 10% profit
(B) 10% loss
(C) 12.5% profit
(D) 12.5% loss
(E) None of these

Answers:

1-Ans : (C)

2-Ans : (D)

3-Ans. (C)

4-Ans. (D)

5-Ans. (A)
Let CP = Rs 100, P = 30.05%
∴ S.P. = Rs 130.05
Discounts = 10%, 15%, 15%∴ M.P. = 130.05 × 100/90 x 100/85 x 100/85 = Rs 200
If discounts are 10% and 15% only
∴ S.P. = M.P. × {(100-d1)/100} x {(100-d2)/100}
=> 200 x 90/100 x 85/100 = Rs. 153

So, Profit = 53%

6-Solution :(B) {192/(x-16)} – 192/x = 2 
=> Speed of the fast Train = 48 kmph

7-Solution : (C) Let the speeds of fast plane and slow planes be x and y m/sec respectively D = s × t
If they move in opposite direction
15 (x + y) = 1200 ⇒ x + y = 80 m/sec … (i)
If they move in same direction, relative speed = x – y m/sec
Time = 60 i.e. 4 times
∴ Speed is (1/4)th x – y = 20 m/sec … (ii)
Solving (i) and (ii),
y = 50 m/sec = 0.05 km/sec

8-Ans. (D)
You are starting from Mumbai at 12:00 noon, so you’ll meet first train which is going to reach Mumbai at 12:30pm or which started from Pune at 8:00am. Also you’ll reach Pune at 4:30pm, so you’ll meet the last train which leaves Pune at 4:00pm.
So in all, you are going to meet all trains which start from Pune at 8:00am, 9:00am, 10:00am, 11:00am, 12:00noon, 1:00pm, 2:00pm, 3:00pm and 4:00pm i.e. 9 in total. option d.

9-Solution : (A)
(D/40) – (D/50) = 1 ⇒ D = 200 kms

10-Solution : (A) C.P. of 70 kg rice = Rs 175
S.P. = 2.75 × 70 =385/2
P =385/2 – 175 =35/2
∴ P% = 35/2 ×1/175 × 100 = 10 %