Question Bank  100 Arithmetic Questions From Previous CAT Papers (Solved)

Speed when no compartments attached = 42
Speed with 9 compartments attached = 24
Reduced speed = 18
18 = k * sqrt(9)
k = 6
Train doesn't move when there are more compartments. so assuming that the speed is reduced by 42
42 = 6 * sqrt(n)
n = 49
For 49 compartments, Engine won't move. So the maximum possible number of compartments = 49  1 = 48
(And no surprise we have 49 also in the option!)

Q40. (CAT 1999)
Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?
a. 550
b. 580
c. 540
d. 570

Let the fixed amount be F and the partly varying amount be p.
F + 25p = 700 * 25
F + 50p = 600 * 50
On solving these equations we get p = 500 and F = 5000
So, for 100 people, we get 5000 + 100(500) = 55000
Hence, average expense = 55000/100 = 550.

Q41. (CAT 1997)
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.At what time did X catch the thief?
a. 3.30 p.m.
b. 3 p.m.
c. 3.15 p.m.
d. None of theseIf another policeman had started the same chase along with X, but at a speed of 60 km/hr, then how far behind was he when X caught the thief?
a. 18.75 km
b. 15 km
c. 21 km
d. 37.5 km

Part 1 : In the 15 minutes, thief gets a head start of 15 km.
Every hour Police man gains 65  60 = 5 km
So to cover 15 km, Police man needs 15/5 = 3 hours.
So Thief will be caught at 12.15 + 3 = 3.15 PMPart 2: Thief's speed is same as of second police man and Thief already has a 15 km head start. So this distance won't change between them.

Q42. (CAT 1997)
After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?
a. 28.56%
b. 35%
c. 22.22%
d. None of these

Let the cost price be 100
SP = 114.28
114.28 = MP * (100  11.11)/100
MP = 114.28 x 100 / (100  11.11) = 128.56
which is 28.56% more than the cost price.

Q43. (CAT 1997)
A dealer buys dry fruits at Rs. 100, Rs. 80 and Rs. 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight, and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit?
a. Rs. 80
b. Rs. 100
c. Rs. 95
d. None of these

cost price = 300 + 320 + 300 = 920 for 12 kg
profit = 460
SP = 920 + 460 = 1380
price per kg = 1380/12 = 115 ( None of the above)

Q44. (CAT 1997)
An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?
a. 36 s
b. 45 s
c. 27 s
d. None of these

Let's take train length be d.
distance covered = d + 2d
relative velocity = 80  40 = 40 kmph = 40 x 5/18 ( 1 km/h = 5/18 m/s)
3d = 40 x 5/18 x 54 = 600
d = 600/3 = 200
To cross 400 m platform  total length covered = platform length + train length = 400 + 200 = 600
600 = t x 80 x 5/18
t = 600 x 18 / ( 5 x 80 ) = 27 seconds.

Q45. (CAT 1997)
The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.
a. 55
b. 60
c. 62
d. Cannot be determined

Total marks = 10 x 80 = 800
Excluding highest and lowest, total marks = 648
sum of highest and lowest = 800  648 = 152
lowest = 152  92 = 60

Q46. (CAT 1997)
A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.
a. 20%
b. 15%
c. 25%
d. None of these

for 4000, 2000x/100 + 2000y/100 = 700
for 5000, 2000x/100 + 1000y/100 = 900
10y = 200, y = 20
x = 15

Q47. (CAT 2002)
Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of mother of the younger boy. The mother of the younger boy is younger to his father by 3 years. Then, what is the age of the younger boy?
a. 3
b. 4
c. 2
d. None of these

Let the ages of the two boys are p and q ( p > q )
Given that q = (pq)^1/3
Age of the father = 10q + p
Age of the mother = (10p + q)/2
10q + p = (10p + q)/2 + 3
19q  8p  6 = 0Both p and q are single digit numbers (age < 10)
and from the equation, p = q^2
So if we go with the options,
if q = 3, then p = 9, 19q  8p  6 # 0 (not ok. should have been 0)
if q = 4 then p = 16 (not ok. p should be single digit)
if q = 2 then p = 4, 19q  8p  6 = 0 (perfect!)

Q48. (CAT 1997)
Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.If his journey, including stoppage, is covered at an average speed of 180 mph, what is the distance between Frankfurt and India?
a. 3,600 miles
b. 4,500 miles
c. 5,580 miles
d. Data insufficientIf X had started the return journey from India at 2.55 a.m. on the same day that he reached there, after how much time would he reach Frankfurt?
a. 24 hr
b. 25 hr
c. 26 hr
d. Data insufficientWhat is X's average speed for the entire journey (to and fro)?
a. 176 mph
b. 180 mph
c. 165 mph
d. Data insufficient

Part 1 : X reaches Boston at 10 AM. At the same moment, time in Frankfurt is 6 AM. Hence, the journey time was 12 hours.
X reaches India at 1 AM. At the same moment, time in Boston is 11 PM. Hence, the journey time was 11 hours.
Waiting time = 2 hours.
So, total time = 12 + 2 + 11 = 25 hours.
Avg speed = 180 mph
Distance = 180 x 25 = 4,500 miles.Part 2 : Total time taken for return journey = Total time for onward journey  1 = 25  1 = 24 hours
Part 3 : Not sufficient data here.

Q49. (CAT 1996)
A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs. 30,000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100.If he is able to sell only 1,200 out of 1,500 watches he has made in the season, then he has made a profit of
a. Rs. 90,000
b. Rs. 75,000
c. Rs. 45,000
d. Rs. 60,000If he produces 1,500 watches, what is the number of watches that he must sell during the season in order to breakeven, given that he is able to sell all the watches produced?
a. 500
b. 700
c. 800
d. 1,000