Aptitude

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

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Question: In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
[A].

75 cu. m

[B].

750 cu. m

[C].

7500 cu. m

[D].

75000 cu. m

Answer: Option B

Explanation:

1 hectare = 10,000 m2

So, Area = (1.5 x 10000) m2 = 15000 m2.

Depth = 5 m = 1 m.
100 20
Volume = (Area x Depth) = 15000 x 1 m3 = 750 m3.
20

Video Explanation: https://youtu.be/dDbVuBzYop8

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

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Question:
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

[A].

12 kg

[B].

60 kg

[C].

72 kg

[D].

96 kg

Answer: Option B

Explanation:

Volume of water displaced = (3 x 2 x 0.01) m3
= 0.06 m3.
Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

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Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

[A].

49 m2

[B].

50 m2

[C].

53.5 m2

[D].

55 m2

Answer: Option A

Explanation:

Area of the wet surface = [2(lb + bh + lh) – lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.

Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:

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Question: Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:
[A].

16 2 %
3

[B].

14 1 %
2

[C].

13 1 %
3

[D].

15%

Answer: Option A

Explanation:

S.P. = 102% of Rs. 600 = 102 x 600 = Rs. 612.
100

Now, P.W. = Rs. 612 and sum = Rs. 688.50.

T.D. = Rs. (688.50 – 612) = Rs. 76.50.

Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.

Rate = 100 x 76.50 % = 16%
612 x 3
4

The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:

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Question:
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:

[A].

Rs. 1800

[B].

Rs. 1450

[C].

Rs. 1360

[D].

Rs. 6800

Answer: Option C

Explanation:

Sum = S.I. x T.D. = 85 x 80 = Rs. 1360.
(S.I.) – (T.D.) (85 – 80)

A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

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Question: A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
[A].

23 days

[B].

37 days

[C].

37

[D].

40 days

Answer: Option C

Explanation:

Whole work is done by A in 20 x 5 = 25 days.
4
Now, 1 – 4 i.e., 1 work is done by A and B in 3 days.
5 5

Whole work will be done by A and B in (3 x 5) = 15 days.

A’s 1 day’s work = 1 , (A + B)’s 1 day’s work = 1 .
25 15
B’s 1 day’s work = 1 – 1 = 4 = 2 .
15 25 150 75
So, B alone would do the work in 75 = 37 1 days.
2 2

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

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Question: X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
[A].

13 1 days
3

[B].

15 days

[C].

20 days

[D].

26 days

Answer: Option A

Explanation:

Work done by X in 8 days = 1 x 8 = 1 .
40 5
Remaining work = 1 – 1 = 4 .
5 5
Now, 4 work is done by Y in 16 days.
5
Whole work will be done by Y in 16 x 5 = 20 days.
4
X’s 1 day’s work = 1 , Y’s 1 day’s work = 1 .
40 20
(X + Y)’s 1 day’s work = 1 + 1 = 3 .
40 20 40
Hence, X and Y will together complete the work in 40 = 13 1 days.
3 3