IBPS PO Mains: Quantitative Aptitude
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
Ans : (C)
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
Ans : (D)
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
Ans. (C)
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
(A) Rs 1.75
(B) Rs 0.875
(C) Rs 1.25
(D) Can not be determined
(E) None of these
Ans. (D)
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
(A) 53%
(B) 62.5%
(C) 72.5%
(D) 68.6%
(E) None of these
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%
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.
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
(A) 30 kmph
(B) 48 kmph
(C) 20 kmph
(D) 25 kmph
(E) None of these
Solution :(B) {192/(x-16)} – 192/x = 2
=> Speed of the fast Train = 48 kmph
=> Speed of the fast Train = 48 kmph
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
(A) 0.04 km/s
(B) 0.03 km/s
(C) 0.05 km/s
(D) 0.02 km/s
(E) None of these
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
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.
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
(A) 8
(B) 10
(C) 13
(D) 9
(E) None of these
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.
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.
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
(A) 200 kms
(B) 180 kms
(C) 400 kms
(D) 300 kms
(E) None of these
Solution : (A)
(D/40) – (D/50) = 1 ⇒ D = 200 kms
(D/40) – (D/50) = 1 ⇒ D = 200 kms
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
(A) 10% profit
(B) 10% loss
(C) 12.5% profit
(D) 12.5% loss
(E) None of these
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 %
S.P. = 2.75 × 70 =385/2
P =385/2 – 175 =35/2
∴ P% = 35/2 ×1/175 × 100 = 10 %
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