CAT 2020 Question Paper With Answers & Explanation

QA

Q. 1 An alloy is prepared by mixing three metals A, B
and C in the proportion 3 : 4 : 7 by volume. Weights
of the same volume of the metals A, B and C are in
the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in
kg, of the metal C is

Q. 2 A person spent Rs 50000 to purchase a desktop
computer and a laptop computer. He sold the desktop
at 20% profit and the laptop at 10% loss. If overall he
made a 2% profit then the purchase price, in rupees,
of the desktop is

Q. 4 Among 100 students, x_{1} have birthdays in January,
x_{2} have birthdays in February, and so on. If x_{0} = max
(x_{1}, x_{2}, …, x_{12}), then the smallest possible value of x0
is

Q. 6 Two persons are walking beside a railway track at
respective speeds of 2 and 4 km per hour in the
same direction. A train came from behind them and
crossed them in 90 and 100 seconds, respectively.
The time, in seconds, taken by the train to cross an
electric post is nearest to

Q. 7 A solution, of volume 40 litres, has dye and water in
the proportion 2 : 3. Water is added to the solution
to change this proportion to 2 : 5. If one-fourths of
this diluted solution is taken out, how many litres of
dye must be added to the remaining solution to bring
the proportion back to 2 : 3?

Q. 12 Veeru invested Rs 10000 at 5% simple annual
interest, and exactly after two years, Joy invested
Rs 8000 at 10% simple annual interest. How many
years after Veeru’s investment, will their balances,
i.e., principal plus accumulated interest, be equal?

Q. 13 A gentleman decided to treat a few children in the
following manner. He gives half of his total stock of
toffees and one extra to the first child, and then the
half of the remaining stock along with one extra to
the second and continues giving away in this fashion.
His total stock exhausts after he takes care of 5
children. How many toffees were there in his stock
initially?

Q. 15 On a rectangular metal sheet of area 135 sq. in, a
circle is painted such that the circle touches two
opposite sides. If the area of the sheet left unpainted
is two-thirds of the painted area then the perimeter
of the rectangle in inches is

Q. 16 A straight road connects points A and B. Car 1 travels
from A to B and Car 2 travels from B to A, both leaving
at the same time. After meeting each other, they
take 45 minutes and 20 minutes, respectively, to
complete their journeys. If Car 1 travels at the speed
of 60 km/hr, then the speed of Car 2, in km/hr, is

Q. 18 A train travelled at one-thirds of its usual speed, and
hence reached the destination 30 minutes after the
scheduled time. On its return journey, the train initially
travelled at its usual speed for 5 minutes but then
stopped for 4 minutes for an emergency. The
percentage by which the train must now increase its
usual speed so as to reach the destination at the
scheduled time, is nearest to

Q. 21 A solid right circular cone of height 27 cm is cut into
two pieces along a plane parallel to its base at a
height of 18 cm from the base. If the difference in
volume of the two pieces is 225 cc, the volume, in
cc, of the original cone is

Q. 22 In a group of people, 28% of the members are young
while the rest are old. If 65% of the members are
literates, and 25% of the literates are young, then
the percentage of old people among the illiterates is
nearest to

Q. 25 Leaving home at the same time, Amal reaches office
at 10:15 am if he travels at 8 km/hr, and at 9:40 am
if he travels at 15 km/hr. Leaving home at 9:10 am,
at what speed, in km/hr, must he travel so as to
reach office exactly at 10 am?

Q. 26 Let A, B and C be three positive integers such that
the sum of A and the mean of B and C is 5. In addition,
the sum of B and the mean of A and C is 7. Then the
sum of A and B is