Research Aptitude Test

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Research Aptitude Test - 16

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Weekly Quiz Competition

Question 1
2 / -0.5

A can do a work in 10 days and B can do the same work in 20 days. They work together for 5 days and then A goes away. In how many, more days will B finish the work?

A
A. 5 days

B
B. 6.5 days

C
C. 10 days

D
D.

Solution

In 5 days the can complete
Remaining is 1/4 part
Question 2
2 / -0.5

In a fort there was sufficient food for 200 soldiers for 31 day. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?

A
A. 12 days

B
B. 10 days

C
C. 8 days

D
D. 6 days

Solution

Man x Day = Man. Day
200 x 31 = 6200
After 27 days
200 x 27 = 5400 Man. Day is finished Remaining = 800
Man Day = 800
80 Day = 800
Day = 10
Question 3
2 / -0.5

Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.

A
A. Rs. 2000

B
B. Rs. 2200

C
C. Rs. 1000

D
D. Rs. 1100

Solution

P = ?, Cl = Rs. 420, R = 10%, T = 2 years.
Question 4
2 / -0.5

A sum of money doubles itself in 5 years. In how many years will it become fourfold (if interest is compounded)?

A
A. 15

B
B. 10

C
C. 20

D
D. 12

Solution

⇒ 4 = [2^1/5 ]^T
⇒ 2² = 2T/5
⇒ T/5 = 2
∴ T = 10 yrs.
Question 5
2 / -0.5

Divided Rs. 6000 into two parts so that simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.

A
A. Rs. 4000, Rs. 2000

B
B. Rs. 5000, Rs. 1000

C
C. Rs. 3000, Rs. 3000

D
D. None of these

Solution

Let one part be Rs. x then
12x = 144000 - 24x
36x = 144000
x = 4000
Question 6
2 / -0.5

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph, Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

A
9 a.m.

B
10 a.m.

C
11 a.m.

D
10.30 a.m

Solution

Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km
Distance covered by B in (x - 1) hours
= 25 (x - 1)km
∴20x + 25 (x - 1) = 110
or 45x = 135 or x = 3.
So, they meet at 10 a.m.
Question 7
2 / -0.5

Two trains are running in opposite directions towards each other with speeds of 54 kmph and 48 kmph respectively. If the length of the train is 250 m and they cross each other in 18 seconds, the length of the other train is

A
A. 145 m

B
B. 230m

C
C. 260 m

D
D. 180 m

Solution

Relative speed = (54 + 48) kmp
Let the length of the other train be x metres
= 1530 or x = 260 m
∴ The length of the other train is 260 m.
Question 8
2 / -0.5

A train travelling at 48 kmph completely crosses- another train having half its length and traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

A
A. 560m

B
B. 400m

C
C. 600 m

D
D. 450 m

Solution

Let the length of the first train be x metres.
Then, the length of the second train is (x/2) metres.
Relative speed = (48 + 42) kmp
or x = 200.
∴ Length of first train = 200m.
Let the length of platform be y metres.
Speed of the first train
= 1800 ⇒ y = 400 m
Question 9
2 / -0.5

A train of length 150 m takes 10 seconds to pass over another train 100 m long coming from the opposite direction, if the speed of the first train be 30 Kmph. the speed of the second train is

A
A. 36 kmph

B
B. 54 kmph

C
C. 72 kmph

D
D. 60 kmph

Solution

Let the speed of the second train be x kmph.
Relative speed = (30 + x) kmph
⇒ x = 60
Question 10
2 / -0.5

If P_o and P_s are the vapour pressures of the solvent and solution respectively and n₁ and n₂ are mole fractions of solvent and solute respectively, then

A
P_s =P_o n₁

B
P_S =n₁ P _s

C
P₀ = n₁ P_S

D
P_S =n₂ P₀

Solution

If P_o and P_s are the vapour pressures of the solvent and solution respectively, n₁ and n₂ are the mole fractions of the solvent and solute respectively, then P_s =P_o n₁ .

According to Raoult 's law, the vapour pressure of a solvent above a solution is equal to the vapour pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present.