Arithmetical Reasoning Questions

Q:

When 5% is lost in grinding Maize, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of Maize, which grows in the country ?

A) 188 million B) 166 2/3 million
C) 192 3/4 million D) None
 
Answer & Explanation Answer: B) 166 2/3 million

Explanation:

5% - 2% = 3%
=> 3% ------ 5 million bags
100% ---- ?
=> 166 2/3 million bags.

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Q:

P, W, Q, X, R, Y, Z and S sit randomly in a circle facing each other. Consider the following information and questions based on it.

 

1. Y sits exactly between Q and R

2. P does not sit next to either X or Z

3. Z is to the immediate right of Q

4. S sits third from left of X and the right of Y.

 

If they all were facing outside the circle, W would be the left of -

A) X B) S
C) P D) Cannot be determined
 
Answer & Explanation Answer: C) P

Explanation:
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Q:

At what time will B catch up with A, if A starts from a place at 11.00 A.M. and travels at a speed of 3.5 kmph, B starts at 1.00 P.M. and travels with speeds of 1 kmph for 1 hour, 2 kmph for the next 1 hour, 3 kmph for the next 1 hour and so on.

A) 8 : 47 pm B) 6 : 40 pm
C) 8 : 42 pm D) 7 : 40 pm
 
Answer & Explanation Answer: D) 7 : 40 pm

Explanation:

At 1 pm ... Distance between A and B = 2x3.5 = 7 kms
at 2 pm .....Distance between A and B = 7 + 3.5 - 1 = 9.5 kms
At 3 pm ....Distance between A and B = 9.5 + 3.5 - 2 = 11 kms.
..
..
..
At 7 pm distance between A and B = 3 kms.
From 7 pm to 8 pm, speed of A = 3.5 kmph
speed of B = 8 kmph
Relative speed = 4.5 kmph

Time taken by B to meet A = 3/4.5 hrs = 30/45 hrs = 120/3 mins = 40 mins.

So meeting time is 7 : 40 PM.

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Q:

The sum of three numbers is 98. If the ratio of the first to the second is 2:3. And that of the second to the third is 5:8, then the second number is:

A) 30 B) 27
C) 23 D) 33
 
Answer & Explanation Answer: A) 30

Explanation:

Then, A:B = 2:3 and B:C = 5:8
= (5 x 3/5) : (8 x 3/5) = 3:24/5
A:B:C = 2:3:24/5
= 10:15:24 => B = 98 x 15/49 = 30.

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Q:

What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks ?

A) 3 B) 5
C) 7 D) 9
 
Answer & Explanation Answer: A) 3

Explanation:
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Q:

If the positions of the first and the fifth digits of the number 14278359 are interchanged, similarly the positions of the second and the sixth digits are interchanged and so on, then which of the following will be the second digit from the right end after the rearrangement ?

A) 5 B) 2
C) 7 D) 4
 
Answer & Explanation Answer: B) 2

Explanation:

Given number is 14278359
As given 1st and 5th digits, 2nd & 6th, 3rd & 7th and 4th & 8th digits are to to be interchanged.
Therfore, the rearranged number is 83591427
Then, the second digit from the right end is 2.

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Q:

Hemavathi cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is fifteen grams in weight. If she has nine pieces of the cake in all with her, how heavy was the original cake ?

A) 240 gms B) 280 gms
C) 180 gms D) 170 gms
 
Answer & Explanation Answer: A) 240 gms

Explanation:

The nine pieces consist of 8 smaller equal pieces and one half cake piece.
Weight of each small piece = 15 g.
So, total weight of the cake = [2 x (15 x 8)]g = 240 g.

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Q:

O and O' are the center of the two circles with radii 7cm and 9cm respectively. The distance between the centers is 20cm. If PQ be the transverse common tangent to the circles, which cuts OO' at X, what is the length of O'X in cm ?

A) 10 B) 6
C) 35/4 D) 45/4
 
Answer & Explanation Answer: D) 45/4

Explanation:

As clear from the figure itself, triangle OQX and triangle O'PX are similar.

So,

OQ/O'P = OX/O'X

=> OX = (7/9)xO'X

And since, OX + O'X = 20

=> (7/9)xO'X + O'X = 20

=> O'X = 45/4

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