AMCAT Sample Questions Quants Solutions 111-120

Ques 111 : Choose the correct answer.
Prabodh bought 30 kg of rice at the rate of Rs. 8.50 per kg and 20 kg of rice at the rate of Rs. 9.00 per kg. He mixed the two. At what price (App.) per kg should he sell the mixture in order to get 20% profit?
Option 1 : Rs. 9.50 Option 2 : Rs. 8.50 Option 3 : Rs. 10.50 Option 4 : Rs. 12.00

30 Kg->8.50*30=255
20kg -> 9*20 =180
so
50Kg=435; 1kg=435/50=8.7.
So CP of 1kg=8.7
now 20% profit it means -> (20/100)*8.7=1.74.
so the final ans is 8.7+1.74="10.44"

Ques 112 : Choose the correct answer.
The cash price of a television is Rs. 4022. A customer paid Rs. 1500 in cash and promised to pay the remaining money in 3 monthly equal installments at the rate of 5% per annum compound interest. What is the value of each installment?
Option 1 : Rs. 926.10 Option 2 : Rs. 903.33 Option 3 : Rs. 928.30 Option 4 : Rs. 940.50

x/(20/21) + x/(20/21)^2 + x/(20/21)^3 = 2522
here x is the monthly installment.
20/21= (1+r/100)
x=926.10

Ques 113 : Choose the correct answer.
The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10000, what is its present population?
Option 1 : 6000 Option 2 : 10000/144 Option 3 : 6400 Option 4 : 7600

10000*(80/100)*(80/100)
=6400

Ques 114 : Choose the correct answer.
A certain sum of money at simple interest becomes Rs. 1062 in 2 years and Rs. 1183.50 in 3½ years. What is rate of interest per annum?
Option 1 : 7% Option 2 : 6% Option 3 : 9% Option 4 : 5%

1062-X=2*X*R/100
1183.50-X=7*X*R/200
X=900
R=9%

Ques 115 : Choose the correct answer.
If the simple interest on a sum at 4% per annum for 2 years is Rs. 80, then the compound interest on the same sum for the same period is:
Option 1 : Rs. 86.80 Option 2 : Rs. 86.10 Option 3 : Rs. 88.65 Option 4 : Rs. 81.60

Ques 116 : Choose the correct answer.
A man covers a distance of 1200 km in 70 days resting 9 hours a day, if he rests 10 hours a day and walks with speed 1½ times of the previous in how many days will he cover 750 km?
Option 1 : 30 Option 2 : 31.25 Option 3 : 31 Option 4 : 33

Case 1:
Total Distance = 1200km
Total time=70*(24-9)=1050
Speed=D/T=1200/1050

Case 2:
Speed = (old speed*1.5)= (1200/1050)*1.5
Distance = 750
Time = Dis/Speed = 750/((1200/1050)*1.5)=437.5
Now resting 10 hrs a day ie. working 14 hrs a day
therfore 437.5/14=31.25 (Answer)

Ques 117 : Choose the correct answer.
A train leaves Delhi at 6.00 a.m. and reaches Agra at 10.00 a.m. Another train leaves Agra at 8.00 a.m. and reaches Delhi at 11.30 a.m. At what time do the two trains cross each other if the distance between Delhi and Agra is 200 km?
Option 1 : 8.45 a.m. Option 2 : 8.56 a.m. Option 3 : 9.20 a.m. Option 4 : 9.56 a.m.

Speed of first=s=200/4=50km/h
Speed of second=S=200/3.5=400/7km/h
Till 8 A.M. first one has already covered 50 x 2=100 Kms
So now both are 100 km apart
They are approaching each other
So relative speed=50+400/7=750/7 Km/h
Time=100/(750/7)=700/750=14/15 hours=14x60/15=56 minutes
So they will cross each other at 8.56A.M

Ques 118 : Choose the correct answer.
How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution of concentrated acid to get a 30 L solution of 78% concentrated acid?
Option 1 : 24 L Option 2 : 22.5 L Option 3 : 6 L Option 4 : 17.5 L

the concentration is given which is wrt 100, hence we can take x lt of 90% and (30-x)of 75%
x*90 + (30-x)*75 = 30*78 hence the ans is 6 liters

Ques 119 : Choose the correct answer.
If x is a positive number and y = x2, then which of the following is true?
Option 1 : y is always more than x Option 2 : x is always more than y Option 3 : x is always equal to y Option 4 : None of these

when x=1 and y=1 then option d is correct.

Ques 120 : Choose the correct answer.
Rajiv has a number x in his mind. He finds out that the square of x is less than x. What is the range of x?
Option 1 : x is more than 0 Option 2 : x is less than 1 Option 3 : x is more than 0, but less than 1 Option 4 : This is not possible

Given,the square of x is less than x i.e ,x^2

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