Quantitative Aptitude Practice Questions (20 – 04 – 2018)

Quantitative Aptitude Practice Questions (20 – 04 – 2018)
Directions (1 – 4): The following table is a record of the performance of 12 students in the school team competitions. There are only three prizes i.e.Winner, 1st runner up and 2nd runner up. Winner, 1st runner up and 2nd runner up are awarded 5, 3 and 1 points respectively.
1. Which team gets the highest points in overall?
a) A
b) B
c) C
d) D
e) Tie between C and B
2. Who got the maximum points in overall?
a) Surendar
b) Neeraj
c) Siva
d) Sandeep
e) Neeraj and surendar both
3. Which student has bagged maximum prizes in all the competitions?
a) Neeraj
b) Suresh
c) Surendar
d) Sandeep
e) Siva
4. Which of the following options contains only the names of the winners of a competition?
a) Surendar, Neeraj, Subash
b) Surendar, Subash, Aakash
c) Surendar, Suresh, Siva
d) Neeraj, Siva, Aakash
e) Neeraj, Siva, Subash
5. Ramesh and Suresh earn Rs. x and Rs. y respectively. Ramesh spends 60% of his earning on rent and utilities, 80% of the remaining for food, Rs 360 for buying a shirt and saves the remaining money. Suresh spends 75% of his earning on rent and utilities, 90% of the remaining for food, Rs 75 for buying a hat and saves the remaining. If the savings of Ramesh is 100% more than the savings of Suresh and their sum of their salaries is Rs 27000, what is the value of x?
a) 12000
b) 15000
c) 18000
d) 11000
e) 14000
6. In a vessel, there is a mixture of apple, orange and mango juices in the ratio of 3 : 5 : 4 respectively. A quantity of 12 litres from the mixture is replaced by 8 litres of apple juice. Thereafter the quantities of apple and orange juices in the resultant mixtures become same. Find out the initial quantity of mixture in the vessel.
a) 90 litres
b) 70 litres
c) 60 litres
d) 80 litres
e) 100 litres
7. Raj likes to cross the moving train before it reaches a station 4 km away from where he is now. He starts from the end of the train and crosses it at a point 2.4 km away from the station. If he moves faster by 18 km/hr, he would cross the train at a point 3 km away from the station. If the train is moving with a speed of 54 km/hr, then what is the length of the train (in m)?
a) 450
b) 500
c) 550
d) 400
e) 350
8. A wholesale shopkeeper purchases rice for Rs. 22 per kg and sells it at Rs. 25 per kg. He also indulges in dishonest dealing by selling y kg instead of 1 kg. A retail shopkeeper purchases goods from him and sells it at Rs. 28/kg. If he faces a loss of 16% because of being cheated, what is the value of y in kg?
a) 0.85
b) 0.9
c) 0.75
d) 0.70
e) 0.65
9. X, Y and Z started a business with their investment in the ratio 2 : 3 : 7. If the total investment is 312000. After 4 months, X invests an additional amount of Rs. 1000 in the business. After 6 months from the start of the business Y and Z invest additional amount of Rs. 2000 and Rs. 1000 respectively. X received 35% of the profit for managing the business and the rest is divided in proportion to their capitals. The amount received by X out of the profit of Rs. 1450000 in all is
a) 567600
b) 665500
c) 577600
d) 656500
e) 676700
10. 5 class A workers and 4 class B workers are assigned a job to paint a circular park. They work for one day and complete painting till half the radius of the circular park. The next day, class B workers go on strike and returns the day after as the management resolves their problems. This creates a delay of 4 hours and 48 min in overall. If their payment is based on their efficiency, what will be the ratio of their pay?
a) 16 : 5
b) 5 : 16
c) 8 : 5
d) 5 : 8
e) 6 : 5
Solutions:
1. C)

Team C gets the maximum points.
2. E)

Surendar and neeraj both gets the maximum points.
3. A) With the help of table in Sol (2)
Neeraj has the maximum number of prizes
1st in weight lifting
2nd in shot put
3rd in both long jump and triple jump
Neeraj has bagged prizes in many competition
4. C) Observing the table in Sol (2) we have Winners of the following competitions
High Jump : Surendar = 162 cm
Long Jump : Surendar = 121 cm
Weight Lifting : Neeraj = 56 kg
Shot put : Sandeep = 1.72 cm
Javelin : Suresh = 7.25 cm
Triple jump : Siva = 312 cm
Option containing only name of the winners is (C)
5. A) Amount spent by Ramesh on rent and utilities = 60/100 × x = 0.6x
Remaining amount left = x 0.6x = 0.4x
Amount spent by Ramesh on food = 80/100 × 0.4x = 0.32x
Remaining amount left = 0.4x 0.32x = 0.08x
Remaining amount after buying a shirt = Savings = 0.08x 360
Amount spent by Suresh on rent and utilities = 75/100 × y = 0.75y
Remaining amount left = y 0.75y = 0.25y
Amount spent by Suresh on food = 90/100 × 0.25y = 0.225y
Remaining amount left = 0.25y 0.225y = 0.025y
Remaining amount after buying a hat = Savings = 0.025y – 75
Given that the saving of Ramesh is 100% more than that of Suresh i.e. twice that of Suresh
0.08x 360 = 2 × (0.025y 75)
0.08x 0.05y = 210      ---- (1)
Total salary received = x + y = 27000      ---- (2)
Solving we get x = 12000 and y = 15000
6. C) Ratio of apple, orange and mango juices = 3 : 5 : 4
Let 12x is the initial quantity, so,
3x 3 + 8 = 5x 5
2x = 10
x = 5
Initial quantity = 12 × 5 = 60 litres
7. D) Let their speed of the man be ‘x’ and the length of the train be ‘L’
Relative speed = x 54
Time taken to cross = Length of train / Relative speed = L / (x 54)
Distance travelled by the man in the same time = Speed × time
4 2.4 = x × L/ (x 54)
(1.6x 86.4) /x = L    1
In second case,
Relative speed = x + 18 – 54 = x – 36
Time taken to cross = Length of train / Relative speed = L / (x 36)
Distance travelled by the man in the same time = Speed × time
4 3 = (x + 18) × L/ (x 36)
(x 36) / (x + 18) = L    2
Equating 1 and 2
(1.6x 86.4) /x = (x – 36) / (x + 18)
1.6x2 – 57.6x – 1555.2 = x2 – 36x
(0.6x2 – 21.6x – 1555.2) ÷ 0.6
x2 – 36x - 2592 = 0
Solving x = 72 or x = -36
Speed cannot be negative,
x = 72
Substituting in equation 2,
L = 36/90 = 0.4 km = 400 m
8. C) Let the retail shopkeeper purchase 1 kg, but originally, he got just y kg
Cost price of the rice = 1 × 25 = Rs. 25
Selling price of rice = y × 28 = Rs. 28y
Loss = 25 28y
Loss% = {(25 28y) /25} × 100
16 = (25 28y) × 4
21 = 28y
y = 21/28 = 0.75
9. B) Let the investment by X be 2s, Y be 3s and Z be 7s
2s + 3s + 7s = 312000
12s = 312000
s = 312000/12 = 26000
Investment of X = 2s = 2 × 26000 = 52000
Investment of Y = 3s = 3 × 26000 = 78000
Investment of Z = 7s = 7 × 26000 = 182000
Ratio of profit = 52000 × 4 + 53000 × 8 : 78000 × 6 + 80000 × 6 : 182000 × 6 + 183000 × 6
632000 : 948000 : 2190000
632 : 948 : 2190
316 : 474 : 1095
Profit of X for managing the business = 35% of 1450000 = 507500
Remaining profit = 1450000 507500 = 942500
Let the share of profit of X from remaining profit be 316t, Y be 474t and Z be 1095t
316t + 474t + 1095t = 942500
1885t = 942500
t = 500
Profit share of X = 316t = 316 × 500 = 158000
Total profit = 507500 + 158000 = 665500
10. A) Let a class A worker complete the work in ‘a’ days and a class B worker complete the work in ‘b’ days
Amount of work done by a class A worker in 1 day = 1/a
Amount of work done by a class B worker in 1 day = 1/b
Amount of work done by 5 class A and 4 class B workers in 1 day = 5/a + 4/b = 1/4 [ Half the radius, quarter the area of the circle]
20/a + 16/b = 1 → 1
So, they would have completed the work in 4 days if the strike did not happen. But, it takes 4 days 4 hours and 48 min due to the strike
Class A workers work for 4 days 4 hours 48 min whereas class B workers work for 3 days 4 hours 48 min
4 hours 48 min = (4/24) + {48/ (60 × 24)} = 0.2 day
Total amount of work done = 4.2 × (5/a) + 3.2 × (4/a)
1 = 21/a + 12.8/b 2
Comparing equations 1 and 2
21/a + 12.8/b = 20/a + 16/b
1/a = 3.2/b
a/b = 1/3.2
Efficiency 1/Time taken
Ratio of their efficiencies = 3.2 : 1 = 16 : 5