AMCAT Sample Questions Quants Solutions 101-110

Ques 101 : Choose the correct answer.
In an examination, 70% of students passed in physics, 65% in chemistry, 27% failed in both subjects. The percentage of students who passed is:
Option 1 : 66% Option 2 : 62% Option 3 : 69% Option 4 : None of these

65% passed in English.
So 35% failed in it.
70% passed in Maths. So 30% failed in it.
Percentage of people not all pass
= Percentage of people failed in E + Percentage of people failed in M - Percentage of people failed in both
That is Percentage of people not all pass = 35 + 30 - 27 = 38%
Percentage of people passed in both = 62%

Ques 102 : Choose the correct answer.
An article was sold for Rs. 2770. Had it been sold for Rs. 3000 there would have been an additional gain of 10%. Cost Price of the article is:
Option 1 : Rs. 2100 Option 2 : Rs. 2200 Option 3 : Rs. 2300 Option 4 : Rs. 2400 Option 5 : None of these

original SP = 2770
Let CP be x
then Gain = (2770 – x)
% gain = (2770 – x)/CP × 100

new SP = 300
original CP be x
then Gain = (3000 – x)
% gain = (3000 – x)/CP × 100

(3000 – x)/CP × 100 – (2770 – x)/CP × 100 = 10
100/CP[(3000 – x) – (2770 – x)] = 10
[(3000 – 2770 )] = 10 CP
100(230) = 10 CP
CP = 2300

Ques 103 : Choose the correct answer.
Rakesh buys a scooter worth Rs. 10,000. He sells it to Mohan at a profit of 10%. If after sometime Mohan sells it back to Rakesh at a loss of 10%, then totally:
Option 1 : Rakesh loses Rs. 100 Option 2 : Rakesh loses Rs. 1100 Option 3 : Rakesh gains Rs. 100 Option 4 : Rakesh gains Rs. 1100 Option 5 : None of these

Rakesh buys it for 10000
sells it at 10% profit
Therefore s.p= 11000
Mohan's C.P= 11000
sells back to Rakesh at 10% loss
Therefore S.P = 9900
Therefore Rakesh's total gain=(1000+(10000-9900))=1100
Rakesh gains Rs.1100

Ques 104 : Choose the correct answer.
The list price of an electric iron is Rs. 300. If two successive discounts of 15% and 10% are allowed, its selling price will be:
Option 1 : Rs. 229.50 Option 2 : Rs.231.50 Option 3 : Rs.232.50 Option 4 : Rs. 234.50 Option 5 : None of these

The list price of an electric iron is Rs. 300. If two successive discounts of 15% and 10%
are allowed, what will be the iron's discounted price?
 
15% = 0.15
1 - 0.15 = 0.85
0.85(Rs. 300) = Rs. 255
10% = 0.1
1 - 0.1 = 0.9
0.9(Rs. 255) = Rs. 229.50

Ques 105 : Choose the correct answer.
The rate of compound interest at which a sum of Rs. 8000 amounts to Rs. 8820 in 2 years, is:
Option 1 : 5% Option 2 : 4% Option 3 : 6% Option 4 : 7% Option 5 : None of these

A=P(1+R/100)^N
8820=8000(1+R/100)^2
441/400=(1+R/100)^2
(21/20)^2=(1+R/100)^2
21/20=1+R/100
R=100/20=5

Ques 106 : Choose the correct answer.
A car is 250 metres behind the bus. The car and bus are moving with speed 60 km/hr and 35 km/hr respectively. The car will be ahead of bus by 250 metres in:
Option 1 : 37 seconds Option 2 : 48 seconds Option 3 : 72 seconds Option 4 : 68 seconds Option 5 : None of these

Ans 72 sec.
Relative speed=60-35=25 Km/hr
For car to be ahead of bus by 250 meter,distance to be covered=250+250=500m=0.5km
So time taken=0.5/25=1/50 Hr or 3600/50=72 seconds

Ques 107 : Choose the correct answer.
Mohan walks a certain distance and rides back in 6 hours and 15 minutes. If he walks both ways he takes 7 hours and 45 minutes. If Mohan rides both ways the time which he will take will be:
Option 1 : 4 hours Option 2 : 19/4 hours Option 3 : 9/2 hours Option 4 : 17/4 hours Option 5 : None of these

W+R=375 minutes(6 hours 15 minutes)
2W=465 minutes(& hours 45 minutes)
2R=?
2(W+R)=375*2=750
2R=750-465=285=19/4

Ques 108 : Choose the correct answer.
Population of a village is eight thousand. If 6% men and 10% women are added, population becomes 8,600, then the number of men in the village was:
Option 1 : 4800 Option 2 : 5000 Option 3 : 5060 Option 4 : 6000

take x male then 8000-x=female
so x*106/100 + (8000-x)*110/100 =8600
by solving we get x=5000(men)

Ques 109 : Choose the correct answer.
If 15 oxen or 20 cows can eat the grass of a field in 80 days, then in how many days will 6 oxen and 2 cows eat the same grass?
Option 1 : 40 Option 2 : 60 Option 3 : 100 Option 4 : 160

15 oxen take 80 day so, 6 oxen take 15*80/6 =200 day
20 oxen also take 80 day so, 2 cow take 20*80/2 =800 day

so question 6 oxen "or"2 cows is wrong i think because takes different time.

if Question is for 6 oxen "and" 2 cows then
together work will be 800*200/(800+200) =160 days

Ques 110 : Choose the correct answer.
At a certain party the ratio of gents and ladies was 1 : 2. But when 2 gents and 2 ladies left the party, the ratio became 1 : 3. How many people were initially present in the party?
Option 1 : 12 Option 2 : 15 Option 3 : 18 Option 4 : 24

Ratio of G & L =1:2 => x : 2x

Two G & Two L are left i.e  =>x-2 : 2x-2

=> x-2 : 2x-2 = 1 : 3
=> x-2/2x-2 = 1/3
=>3x-6 = 2x-2
=> X=4 (Gents)
=> 2x=8 (Ladies)
:. Total people = 12

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