Aptitude and Reasoning Questions

Q:

Three taps I, J and K can fill a tank in 20,30and 40 minutes respectively. All the taps are opened simultaneously and after 5 minutes tap A was closed and then after 6 minutes tab B was closed .At the moment a leak developed which can empty the full tank in 70 minutes. What is the total time taken for the completely full ?

A) 24.315 minutes B) 26.166 minutes
C) 22.154 minutes D) 24 minutes
 
Answer & Explanation Answer: B) 26.166 minutes

Explanation:

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120


For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120


So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120


Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes

 

Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.

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13 9722
Q:

The number of permutations of the letters of the word 'MESMERISE' is  ?

A) 9!/(2!)^{2}x3! B) 9! x 2! x 3!
C) 0 D) None
 
Answer & Explanation Answer: A) 9!/(2!)^{2}x3!

Explanation:

n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = 9!(2!)2×3!

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

3 9718
Q:

A person is asked to put in a basket one apple when ordered 'one', one guava when ordered 'two', one orange whe ordered 'three' and is asked to take out from the basket one apple and one guava both when ordered 'four'. The ordered sequence executed by the person is as follows :

1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4


1. How many apples will be there in the basket at the end of the above order sequence ?
      (a) 4     (b) 3     (c) 2    (d) 1


2. How many fruits will be there in the basket at the end of the above order sequence ?
      (a) 13   (b) 17   (c) 9    (d) 11

Answer

1. Answer (c)


Each time we order 1, one apple is added to the basket but each time when 4 is ordered, one apple is removed from it.


Required number of apples = number of 1's - number of 4's = 6 - 4 = 2


2. Answer (d)


Each time we order 1, 2 or 3, one fruit is added to the basket but when ever we order 4, two fruits are removed from it.


Required number = Number of 1's + Number of 2's + Number of 3's - 2 x (Number of 4's)


= 6 + 6 + 7 - (2x4)
= 19 - 8
= 11.

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13 9709
Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.15 is

A) 0 B) 37.5
C) 27 D) 15
 
Answer & Explanation Answer: B) 37.5

Explanation:

Angle between hands of a clock

 

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

 

=> 30H-M5+M2 degrees

 

Here H = 4, M = 15 and the minute hand is behind the hour hand.

 

Hence the angle

 

 = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

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Filed Under: Clocks
Exam Prep: GATE , CAT , Bank Exams , AIEEE
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24 9706
Q:

If 200 cats kill 200 mice in 200 days, then 8 cats would kill 8 mice in how many days ?

A) 8 days B) 200 days
C) 800 days D) 1 day
 
Answer & Explanation Answer: B) 200 days

Explanation:

As given
200 cats kill 200 mice in 200 days
1 cats kill 1 mouse in 200 days
Then
8 cats kill 8 mice in 200 days.

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Filed Under: Arithmetical Reasoning
Exam Prep: AIEEE , Bank Exams , CAT
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10 9685
Q:

P alone can do a piece of work in 24 days. The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work. How many days are required to complete by P and Q working together ?

A) 9 3/5 days B) 7 days
C) 6 3/7 days D) 8 days
 
Answer & Explanation Answer: A) 9 3/5 days

Explanation:

Let the total work be 'W'

As per the given information,

P can complete the work 'W' in 24 days.

=> one day work of P = W/24

And also given that,

The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work

=> PW/3 = QW/2

=> P's

1 day =    W/24

   ?    =      W/3

=>  ?  = 24W/3W  = 8

=> QW/2 = 8 days

=> Q alone can complete the work W in 16 days

=> P + Q can complete the work in

1/24 + 1/16 = 5/48

=> 48/5 days = 9 3/5 days.

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Filed Under: Time and Work
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Bank Clerk , Bank PO

18 9680
Q:

Ramesh spent Rs. 38460 on the renovation of his home, Rs. 24468 on buying furniture and remaining 28% of the total amount he had as cash with him. What was the total amount ?

A) 87400 B) 92520
C) 88470 D) 90150
 
Answer & Explanation Answer: A) 87400

Explanation:

Let X be the total amount with Ramesh

Given 28% of X = Cash remaining

=> Amount spent = 72% of X = 38460 + 24468 = 62928

=> 72% of X = 62928

=>  X = ?

=> X = 87400

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Filed Under: Percentage
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

9 9676
Q:

Pipe K fills a tank in 30 minutes. Pipe L can fill the same tank 5 times as fast as pipe K. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow ?

A) 3 minutes B) 2 minutes
C) 4 minutes D) 5 minutes
 
Answer & Explanation Answer: D) 5 minutes

Explanation:

Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by K = 3 liters.
Capacity of tank filled in 1 minute by L = 15 liters.
Therefore, capacity of the tank filled by both K and L in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.

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11 9676