Research Aptitude Test

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Research Aptitude Test - 11

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Weekly Quiz Competition

Question 1
2 / -0.5

Apurva can do a piece of work in 12 days. Apurva and Amit completed the work together and were paid Rs. 54 and Rs. 81 respectively. How many days must they have taken to complete the work together?

A
A. 4 days

B
B. 4.5 days

C
C. 4.8 days

D
D. 5 days

Solution

Payment ratio = 54:81
days work = 1/12 : 1/x
54 : 81 = 1/12 : 1/x
together they will take = (12 x 8)/(12 + 8) = 4.8 days
Question 2
2 / -0.5

If 12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days, compare the daily work done by a man with that done by a boy?

A
A. 1 : 2

B
B. 1 : 3

C
C. 2 : 1

D
D. 3 : 1

Solution

12 M + 16 B = 1/5 …..(i)
13 M + 24 B = 1/4 ……(ii)
Also, 36 M + 48 B = 3/5
26 M + 48 B = 2/4
10 M = 1/10, M = 1/100
from eq (1) B = 1/200 , M : B = 2 : 1
Question 3
2 / -0.5

15 men could finish a piece of work in 210 days. But at the end of 100 days, 15 additional men are employed. In how many more days will the work be complete?

A
A. 80 days

B
B. 60 days

C
C. 55 days

D
D. 50 days

Solution

Man x Day = Man . Day
15 x 210 = 3150, so after 100 days
15 x 100 = 1500 will be completed
remaining work = 1650 Man . Day
Man . Day = 1650
30. Day - 1650
Day = 55
Question 4
2 / -0.5

If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years in Rs. 48, then the principal amount must be

A
Rs. 550

B
Rs. 500

C
Rs. 375

D
Rs. 400

Solution

Here P = ?, R = 20%, T = 3 year Difference Rs. 48
ci = A-P
ci =
On solving P = 375.
Question 5
2 / -0.5

Raju lent Rs. 400 to Ajay for 2 years, and Rs, 100 to Manoj for 4 years and received together from both Rs. 60 as interest. Find the rate of interest, simple interest being calculated.

A
A. 5%

B
B. 6%

C
C. 8%

D
D. 9%

Solution
Question 6
2 / -0.5

It a certain sum of money becomes double at simple interest in 12 years, what would be the rate of interest per annum?

A

B
10

C
12

D
14

Solution

p=2x
so si=p-initial
si=2x-x
si=x
Question 7
2 / -0.5

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is

A
A. 48 kmph

B
B. 54 kmph

C
C. 66 kmph

D
D. 82 kmph

Solution

Let the speed of the second train be x kmph Relative speed = (x + 50) kmph
Distance covered = (108+ 112) = 220 m.
or x = 82 kmph
Question 8
2 / -0.5

A train B speeding with 120 kmph crosses another train C, running in the same direction in 2 minutes. If the lengths of the trains B and C be 100 m and 200m respectively, what is the speed of the train C?

A
A. 111 kmph

B
B. 127 kmph

C
C. 123 kmph

D
D. 29 kmph

Solution

Let the speed of train C be x kmph.
Speed of B relative to C = (120 - x)
Distance covered = (100 4 200)m = 300 m.
⇒ 5400 = 120(600-5x) ⇒ x = 111.
Question 9
2 / -0.5

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is

A
A. 72 m

B
B. 54 m

C
C. 50 m

D
D. 45 m

Solution

Given
Speed of the first person = 2 km/h
Speed of the second person = 4 km/h
Train taken to overtake the first person = 9 sec
Train taken to overtake the second person = 10 sec
Formula Used:
Speed = Distance/Time
km/h × 5/18 = m/sec
Concept used:
When two bodies move in the same direction, then
Relative speed = Difference of their speeds
Calculation:
Let the length and the speed of a train be L and V respectively.
Speed of the first person = 2 × 5/18 = 5/9 m/sec
Speed of the second person = 4 × 5/18 = 10/9 m/sec
Relative speed of the train and the first person = (V – 5/9) m/sec
⇒ V – 5/9 = L/9
⇒ V = L/9 + 5/9 ----(1)
Relative speed of the train and the first person = (V – 10/9) m/sec
⇒ V – 10/9 = L/10
⇒ V = L/10 + 10/9 ----(2)
Equating equation (1) and equation (2),
⇒ L/9 + 5/9 = L/10 + 10/9
⇒ L/9 – L/10 = 10/9 – 5/9
⇒ (10 × L – 9 × L)/(10 × 9) = (10 – 5)/9
⇒ (10L – 9L)/90 = 5/9
⇒ L = 5/9 × 90
⇒ L = 50 m
∴ The length of the train is 50 m.
Question 10
2 / -0.5

A square closed loop of area A, lying in the horizontal plane is moving horizontally with velocity v in a uniform vertical magnetic field B. Which one of the following statements is FALSE?

A
There is current in the loop even though there is no battery (or any other voltage source)

B
The work done in moving the coil is being converted to the current in the coil

C
The current is being generated because the magnetic field is doing the work.

D
The emf generated is proportional to the velocity of the coil (e) the emf generated is proportional to the magnetic field strength

Solution

A. True, EMF will be induced by Motional EMF
B. True, Conservation of Work &Energy. Coz,,Work-done by Magnetic Field is zero.
C. False, always work done by Magnetic Field is Zero cozy direction of Force and Displacement are Perpendicular so, Dot Product is Zero always.
D. True, E = [V x B. dl] where, V = Velocity and E = EMF
E. True, E = (V x B), dl where B = Magnetic Field and E = EMF