Simplification- Aptitude Questions and Answers

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Ram went to the market and bought a mathematical book and two pencils for Rs 165. Rahim went to the market and bought the same book and the same 10 pencils for Rs 170. The value of each pencil is?

A)
0.5

B)
1

C)
0.75

D)
2


Correct Answer :

0.5


Explanation :

Let the price of book is X and pencil is Y.

X+2*Y=165
X+10*Y=169

After resolving above equetion 8*Y=4
hence, price of pencil is = 0.5

A man has some chicken and some cow, if the ratio of the number of head and the number of feet is 12: 35, then what should be the number of chickens, if the number of head is only 48?

A)
28

B)
26

C)
24

D)
22


Correct Answer :

26


Explanation :

As given, the ratio of the number of head and the number of feet =12 : 35 and the number of head is 48-
So 12*P=48
P=4

Hence, the number of feet = 35*4 =140
Now,Let the number of chickens is X and cows is Y.
So,
X+Y=48
2X+4Y=140
After resolving above equetion X=26

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 : 2 : 3 : 4. If the loss in total value of the diamond was 70000 what was the price of the original diamond?

A)

100000


B)

140000


C)

150000


D)

175000



Correct Answer :

100000


Explanation :

Let the weights of the pieces of diamond are x, 2x, 3x, 4x.
Total weight of original diamond = 1x + 2x + 3x + 4x = 10x
as is given Cost ∝ (weight)2
Total cost of original diamond = (10x)2 = 100x2 ..…(i)
Now, Cost of each piece = x 2, 4x 2, 9x 2, 16x 2
Total cost pieces = x2(1 + 4 + 9 + 16) = 30x2 …..(ii)

Total loss = 100x2 - 30x2 = 70x2
But total loss = 70000
70x2 = 70000
x2 = 1000

Total cost of original diamond = 100x2
= 100 * 1000 [ x2 = 1000]
= 100000

The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the square of these two numbers?

A)

1024


B)

1256


C)

1536


D)

1640



Correct Answer :

1536


Explanation :

Let the number are x and 5x
Now, (x )(5x ) = 320
5x2 = 320
x2 = 64
x = 8

Therefore Numbers are 8 and 40.
Hence, difference between their squares= (40)2 - (8)2 = 1600 - 64 = 1536

A man left 1/3 rd of his property to his wife and 3/5 th of the remainder to his daughter. He gave the rest to his son who received Rs. 6400/-. How much was his original property worth?

A)

18000


B)

20000


C)

22000


D)

24000



Correct Answer :

24000


Explanation :

Let total property of man= x
His widow gets = x/3
His daughter gets = 3/5 *[x − (x/3)]
=3/5 *(2x/3)=2x/5

His son's property = x−[(x/3)+(2x/5)]
6400 = x−(11x/15)
6400 = (15x−11x)/15
6400*15 = 4x
x = 1600*15
x=24000

Hence, total property=24000

The sum of the digits of a two-digit number is 11. The number obtained by interchanging its digits exceeds the given number by 27. Find the number?

A)
47

B)
56

C)
38

D)
58


Correct Answer :

47


Explanation :

Let x be units digit and y be tens digit.then number is 10y + x
As given,
x + y = 11 ----eq1
10x + y = 10y + x + 27----eq2

from eq2
9x -9y = 27
x - y = 3 ----eq3

by adding eq1 and eq3
2x = 14
x = 7
Substitute x in eq1
7 + y =11
y = 4

Therefore, the number is 10x + y = 10*4 + 7 = 47

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