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

By what number should we multiply -1/5 so that the product may be 9/25?

A)

5/9


B)

-5/9


C)

-9/5


D)

9/5



Correct Answer :

-9/5


Explanation :

Let the number be x ,then
-1/5 * x = 9/25
x = 9*5 / 25*-1
x = 45/ -25
x = - 45/25
x = - 9/5
Hence the number is -9/5

Aamir and Birju can cut 5000 g of wood in 20 min. Birju and Charles can cut 5000 g of wood in 40 min. Charles and Aamir can cut 5 kg of wood in 30 min. How much time Charles will take to cut 5 kg wood alone?

A)
120 min

B)
48 min

C)
240 min

D)
120/7 min


Correct Answer :

240 min


Explanation :

5000g = 5kg

Let Aamir, Birju and Charles alone can complete the work in A, B and C minutes respectively, then
work done in one min by A+B=1/20, B+C=1/40, C+A=1/30
solving the above equations,
A+B+ B+C+ C+A= 1/20+ 1/40+ 1/30
2A + 2B + 2C = 6+3+4 /120
2A + 2B + 2C = 13/120
A + B + C = 13/240

work done in one min by C = (A+B+C) - (A+B)
=> 13/240 - 1/20
=> 1/240
So Charles alone can complete the work in 240 min.

Assume that a sum of money is divided equally among n girls. Each girl will receive $60. If another girl is added to the group and the sum is divided equally among all the girls, each child girl gets a $50 share. What is the sum of money?

A)
$3000

B)
$300

C)
$110

D)
$10


Correct Answer :

$300


Explanation :

As is given, 60*n = 50*(n+1)
=> n=5

∴Sum of the money = 60*n= 60*5=>300
So, the correct answer is 300

What least value must be assigned to * so that the number 197*5462 is divisible by 9?

A)

2


B)
3

C)
4

D)
8


Correct Answer :

2


Explanation :

Let the missing digit be x
Sum of digits = (1+9+7+x+5+4+6+2)=34+x
For 34+x to be divisible by 9 , x must be replaced by 2
The digit in place of x must be 2.

When we multiply a certain two digit number by the sum of its digits , 405 is achieved. If we multiply the number written in reverse order of the same digits by the sum of the digits, we get 486. Find the number?

A)

81


B)
45

C)
36

D)
12


Correct Answer :

45


Explanation :

Let the number be x y.
When we multiply the number by the sum of its digit 405 is achieved.

(10x+y)(x+y)=405....................1

If we multiply the number written in reverse order by its sum of digits we get 486.

(10y+x)(x+y)=486......................2

dividing 1 and 2
(10x+y)(x+y)/(10y+x)(x+y) = 405/486
10x+y / 10y+x = 5/6
60x+6y = 50y+5x
55x = 44y
5x = 4y
x = 4y/5
now put the value in eq 1
(10x+y)(x+y)=405....................1
(10*4y/5+ y)(4y/5 + y)=405
(9y)(9y/5)=405
81*y^2/5 = 405
y^2 = 25
y=5
so X=4y/5 = 4

The number is 45

The sum of all possible two digit numbers formed from three different one digit natural numbers when divided by the sum of the original three numbers is equal to?

A)

18


B)
22

C)
36

D)
45


Correct Answer :

22


Explanation :

Let the one digit numbers x,y,z
Sum of all possible two digit numbers
=>(10x+y)+(10x+z)+(10y+x)+(10y+z)+(10z+x)+(10z+y) = 22(x+y+z)
Therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22.

A number being successively divided by 3,5,8 leaves remainder 1,4,7 respectively. Find the respective remainders if the order of divisors are reversed?

A)

3, 2, 4


B)
4, 4, 4

C)
6, 4, 2

D)
5, 3, 2


Correct Answer :

6, 4, 2


Explanation :

Let the quotient be q .
n=3(5(8q+7)+4)+1
=3(40q+39)+1
=120q+117+1
=120q+118.
Now, if it is divided by 8.
We have 8(15q+14)+6, Remainder will be 6.
And if 15q+14 is divisible by 5. Remainder will be 4.
And if 3q+2 is divisible by 3. Remainder will be 2.
Hence, will be the remainder, 6,4,2.

The arithmetic mean of two numbers is smaller by 24 than the larger of the two numbers and the GM of the same numbers exceeds by 12 the smaller of the numbers. Find the numbers?

A)

6,54


B)
8,56

C)
12,60

D)
7,55


Correct Answer :

6,54


Explanation :

Let the numbers be a,b where a is smaller than b.
The AM of two numbers is smaller by 24 than the larger of the two numbers.
AM=b-24

AM of two numbers is a+b/2
=>a+b/2 = b-24
a+b = 2b-48
a = b-48
b = a + 48...................1

The GM of the two numbers exceeds by 12 the smaller of the numbers
GM = a+12

GM of two numbers is (ab)^1/2
=>(ab)^1/2= a+12
=>a*b = a^2 + 24*a + 144

from eq...1 b=a+48
a*(a + 48) = a^2 + 24*a + 144
a^2 + 48*a = a^2 + 24*a + 144
24*a = 144
a=6

Therefore, b=a+48=54

The sum of squares of the digits constituting a positive two digit number is 13, If we subtract 9 from that number we shall get a number written by the same digits in the reverse order. Find the number?

A)

65


B)
56

C)
45

D)
32


Correct Answer :

32


Explanation :

Let the digit number be x y.
given that x^2+y^2=13

And, num(x, y)-9= num(y, x)
10x+y-9=10y+x
9x-9y=9
x-y=1 ............e1

(x-y)^2 =x^2+y^2-2xy
1 =13-2xy
2xy = 12
xy = 6

x^2+y^2=13
(x+y)^2-2xy=13
(x+y)^2=13+2*6
(x+y)^2=13+12
(x+y)^2=25
(x+y)=5 .............e2

from e2+e1
(x+y) + (x-y) = 5+1
x=3
from e2-e1
(x+y) - (x-y) = 5-1
y=2

Therefore the number is, xy = 32

If we add the square of the digit in the tens place of the positive two digit number to the product of the digits of that number we get 52,and if we add the square of the digit in the unit's place to the same product of the digits we get 117.Find the two digit number?

A)

18


B)
28

C)
39

D)
49


Correct Answer :

49


Explanation :


Let n(x,y) be two digit number
n(x,y)=10x+y
(square of of digits in ten’s place)+(product of digits)=52
x^2+xy=52
x(x+y)=52....................1

(square of digit in unit place)+(product of digits)=117
y^2+xy= 117
y(x+y)=117.........................2

dividing 1 and 2
x(x+y)/y(x+y) = 52/117=4/9
x/y=4/9

it is clear that two digit number is n(x,y),10x+y = 49

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