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11. Raj and Madan appeared in an examination. If the difference of their marks is 60 and percentage difference of their marks is given as 30. Find the full marks for which examination has been held.
  A.  150
  B.  200
  C.  250
  D.  300
     
   
View Answer

Shortcut:
If the value of absolute difference and percentage difference of two items X and Y are given, then the total value is given by
Value of absolute difference / Difference in percent
x 100
Here, Value of absolute difference means difference of their marks = 60, Difference in percent of their marks = 30
Using these value in shortcut, we get:
Full Marks =
60 / 30
x 100 = 200

12. A and B appeared in an examination. If the difference of their marks is 35 and percentage difference of their marks is given as 7%. Find the full marks for which examination has been held.
  A.   500
  B.   450
  C.   550
  D.  400
     
   
View Answer

Shortcut:
If the value of absolute difference and percentage difference of two items X and Y are given, then the total value is given by
Value of absolute difference / Difference in percent
x 100
Here, Value of absolute difference means difference of their marks = 35, Difference in percent of their marks = 7
Using these value in shortcut, we get:
Full Marks =
35 / 7
x 100 = 500

13. One type of liquid contains 25% of milk, the other contains 30% of milk. A can filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of milk in the new mixture.
  A.  23%
  B.  29%
  C.  25%
  D.  27%
     
   
View Answer

Shortcut:
If one type of liquid contains A% of milk, the other contains B% of milk. A person fills a cane with x parts of the first liquid and y parts of the second liquid. Then, percentage of milk in the new mixture is given by
xA + yB / x + y

Here, A% = 25%, B% = 30%, x = 6, y = 4
Using these value in shortcut, we get:
New Mixture =
6x25 + 4x30 / 6 + 4
=
150 + 120 / 10
=
270 / 10
= 27%

14. The daily wage is increased by 20% and a person now gets Rs. 24 per day. What was his daily wage before the increase?
  A.  Rs 22
  B.  Rs 18
  C.  Rs 20
  D.  Rs 25
     
   
View Answer

Shortcut:
Original daily wage is given by
Increased daily wage / 100 + percentage increase
x 100
Here, Increased daily wage = Rs 24, Percentage increase = 20%
Using these value in shortcut, we get:
Required value =
24 / 100 + 20
x 100 =
24 / 120
x 100 =
1 / 5
x 100 = 20
Hence, Rs 20 was his daily wage before increase.

15. The daily wage is decreased by 15% and a person now gets Rs 17 per day. What was his daily wage before the decrease?
  A.  Rs 15
  B.  Rs 20
  C.  Rs 25
  D.  Rs 30
     
   
View Answer

Shortcut:
Original daily wage is given by
Decreased daily wage / 100 − percentage decrease
x 100
Here, Decreased daily wage = Rs 17, Percentage decrease = 15%
Using these value in shortcut, we get:
Required value =
17 / 100 − 15
x 100 =
17 / 85
x 100 =
1 / 5
x 100 = 20
Hence, Rs 20 was his daily wage before decrease.

16. Due to fall in manpower, the production in a factory decreases by 25%. By what percent should the working hours be increased to restore the original production?
  A.  33
1 / 3
%
  B.  31
1 / 3
%
  C.  35
1 / 3
%
  D.  33
1 / 2
%
     
   
View Answer

Shortcut:
Required percentage increase in working hours is given by
Decreased production percentage / 100 − Decreased production percentage
x 100
Here, Decreased production percentage = 25%
Using these value in shortcut, we get:
Required % =
25 / 100 − 25
x 100 =
25 / 75
x 100 =
100 / 3
= 33
1 / 3
%

17. Due to increase in manpower, the production in a factory increases by 25%. By what per cent should the working hour be decreased to restore the original production?
  A.  21%
  B.  25%
  C.  18%
  D.  20%
     
   
View Answer

Shortcut:
Required percentage decrease in working hours is given by
Increased production percentage / 100 + increased production percentage
x 100
Here, Increased production percentage = 25%
Using these value in shortcut, we get:
Required % =
25 / 100 + 25
x 100 =
25 / 125
x 100 =
1 / 5
x 100 = 20%

18. Two numbers are respectively 20% and 50% more than a thrid. What percentage is the first of the second?
  A.  70%
  B.  75%
  C.  80%
  D.  85%
     
   
View Answer

Shortcut:
If two values are respectively a% and b% more than a third value, then the first value is
100 + a / 100 + b
x 100% of the second value.
Here, a = 20, b = 50
Using these value in shortcut, we get:
Required value =
100 + 20 / 100 + 50
x 100 =
120 / 150
x 100 =
12 / 15
x 100 =
4 / 5
x 100 = 4 x 20 = 80
Hence, first value is 80% of the second value.

19. Two numbers are respectively 25% and 50% more than a thrid. What percentage is the second of the first?
  A.  120%
  B.  125%
  C.  115%
  D.  110%
     
   
View Answer

Shortcut:
If two values are respectively a% and b% more than a third value, then the second value is
100 + b / 100 + a
x 100% of the first value.
Here, a = 25, b = 50
Using these value in shortcut, we get:
Required value =
100 + 50 / 100 + 25
x 100 =
150 / 125
x 100 =
6 / 5
x 100 = 6 x 20 = 120
Hence, second value is 120% of the first value.

20. Two numbers are respectively 30% and 40% less than a third number. What per cent is the second of the first?
  A.  95
5 / 7
%
  B.  75
5 / 7
%
  C.  85
1 / 7
%
  D.  85
5 / 7
%
     
   
View Answer

Shortcut:
If two values are respectively a% and b% less than a third value, then the second value is
100 − b / 100 − a
x 100% of the first value.
Here, a = 30, b = 40
Using these value in shortcut, we get:
Required value =
100 − 40 / 100 − 30
x 100 =
60 / 70
x 100 =
6 / 7
x 100 = 85
5 / 7

Hence, second value is 85
5 / 7
% of the first value.

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