Research Aptitude Test

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Research Aptitude Test - 21

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Weekly Quiz Competition

Question 1
2 / -0.5

A cistern is normally filled in 5 hours. However, it takes 6 hours when there is leak in its bottom. If the cistern is full, in what time shall the leak empty it?

A
A. 6 h

B
B. 5 h

C
C. 30 h

D
D. 15 h

Solution

In one hour 1/5 part is filled now leak can empty in x hour then

⇒ 1/30 = 1/x , x = 30 hours
Question 2
2 / -0.5

Pipe A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the time in which A and B will fill the cistern separately will be respectively?

A
A. 15 min, 20 min

B
B. 15 min, 10 min

C
C. 10 min, 15 min

D
D. 25 min, 20 min

Solution

Let pipe A can fill in x and pipe B in x+5 minutes

x = 10, x + 5 = 15
Question 3
2 / -0.5

There are two pipes in a tank. Pipe A is for filling the tank & Pipe B is for emptying the tank. If A can fill the tank in 10 hours and B can empty the tank in 15 hours then find how many hours will it take to completely fill a half empty tank?

A
A. 30 hours

B
B. 15 hours

C
C. 20 hours

D
D. 33.33 hours

Solution

So it takes 30 hours to fill the tank and 15 horse to fill half the tank
Question 4
2 / -0.5

There are three Taps A, B and C in a tank. They can fill the tank in 10 hrs, 20 hrs and 25 hrs respectively. At first, all of them are opened simultaneously. Then after 2 hours tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by Tap A alone. Find the percentage of the work done by Tap A by itself.

A
A. 32%

B
B. 52%

C
C. 75%

D
D. None of these

Solution

So remaining part after 5 hour is

32/10 = 3.2 hours

% of work done by A
Question 5
2 / -0.5

A sum-of money placed at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?

A
A. 9 years

B
B. 8 years

C
C. 27 years

D
D. 7 years

Solution

Let sum = x

⇒ 8 = [2^1/3 ]T

⇒ 2³ = 2^T/3

⇒ T/3 = 3

∴ T = 9 yrs.

Alternative:

If a certain sum of money becomes ‘m’ times in ‘y’ years. Then it will become (mⁿ ) times in ‘n x y’ years. Hence 2³ in 3 x 3 = 9 years,
Question 6
2 / -0.5

A sum of money becomes 7/4 of itself in 6 years at a certain rate of simple interest. Find the rate of interest.

A
A. 12%

B
B. 12.5%

C
C. 8%

D
D. 14%

Solution

Let sctm be x

T = 6 Years , R = ?
Question 7
2 / -0.5

A sum of Rs. 600 amounts to Rs. 720 in 4 years at simple interest. What will it amount to if the rate of interest is increased by 2%?

A
A. Rs. 648

B
B. Rs. 768

C
C. Rs. 726

D
D. Rs. 792

Solution

P = Rs. 600, A = Rs. 720

T = 4 years, R = ?

at 7% Rate

A = 600 + 168 = 768
Question 8
2 / -0.5

A man sees a train passing over a bridge 1 km long. The length of the train is half that of the bridge, if the train clears the bridge in 2 minutes, the speed of the train is

A
A. 30 km/h

B
B. 45 km/hr

C
C. 50 km/hr

D
D. 60 km/hr

Solution

Distance travel in 2 minute

Distance covered in hour

∴ Speed of the train = 45 km/hr
Question 9
2 / -0.5

Helium is two times heavier than H₂ , The average kinetic energy per molecule for helium at 300K is

A
twice as H2

B
same as H2

C
half as H2

D
one fourth of H2

Solution

Kinetic energy per mole or per molecule of a gas depends only on the temperature and not on the nature of the gas.

KE=2/3 RT

So, average kinetic energy of a helium atom is the same as that of a hydrogen molecule.
Question 10
2 / -0.5

When I was a child, there used to be a fair in my town during the Diwali and Eid festivities. Among the many things I saw was a strange puppet show. There were three puppets, one of a man, another of a woman and the third one of a rakshasa (demon). Whenever the rakshasa was brought close to the woman, she would turn her face away. But when the man was brought close to her, she would turn back and face the man.

I and my friends looked at this show and argued for hours what caused the woman to turn her face. Choose one or more of the options below about my childhood experience above:

Q. If there were magnets fixed in the heads the puppets inside the head such that one end of the magnet was at the mouth (M) and the other at the back of the head (B), then the arrangement of the north (N) and south (S) poles of the magnets must be like:

A
A. man: M-N, B-S; woman: M-N, B-S; demon: M-N, 8-S

B
B. man: M-N, B-S; woman: M-S, B-N; demon: M-S, B-N

C
C. man: M-S, B-N; woman: M-S, B-N; demon: M-S, B-N

D
D. man: M-S, B-N; woman: M-N, B-S; demon: M-S, B-

Solution

Woman Head & demon Head Repels means, they must have Similar Poles coz, Similar Poles Repels Hence option 4 got Rejected, now after Turning, Woman Back & Man Head must Repel means They must be Similar So, Option 1, 3 got Rejected also. Hence, option 2 is Correct.