__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)

⇒ 1.6x

^{2}– 57.6x – 1555.2 = x^{2}– 36x
⇒ (0.6x

^{2}– 21.6x – 1555.2) ÷ 0.6
⇒ x

^{2}– 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