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21. Two numbers are respectively 25% and 40% less than a third number. What per cent is the first of the second?
  A.  120%
  B.  115%
  C.  135%
  D.  125%
     
   
View Answer

Shortcut:
If two values are respectively a% and b% less than a third value, then the first value is
100 − a / 100 − b
x 100% of the second value.
Here, a = 25, b = 40
Using these value in shortcut, we get:
Required value =
100 − 25 / 100 − 40
x 100 =
75 / 60
x 100 =
5 / 4
x 100 = 5 x 25 = 125
Hence, first value is 125% of the second value.

22. Two numbers are respectively 20% and 25% of a third number. What percentage is the first of the second?
  A.  75%
  B.  85%
  C.  80%
  D.  70%
     
   
View Answer

Shortcut:
If X is a% of Y, and Z is b% of Y, then X is
a / b
x 100% of Z.
Here, a = 20, b = 25
Using these value in shortcut, we get:
Required value =
20 / 25
x 100 =
4 / 5
x 100 = 4 x 20 = 80
Hence, X is 80% of the Z.

23. A man loses 12
1 / 2
% of his money and after spending 70% of the remainder, he is left with Rs 210. How much had he at first?
  A.  Rs 820
  B.  Rs 800
  C.  Rs 810
  D.  Rs 830
     
   
View Answer

Shortcut:
If a% of a quantity is taken by the first, b% of the remaining is taken by the second and c% of the remaining is taken by the third person. Now, if Rs Z is left in the fund, then there was
Z x 100 x 100 x 100 / (100 − a)(100 − b)(100 − c)
fund in the begining.
Here, Z = 210, a = 12
1 / 2
or 12.5, b = 70
Using these value in shortcut, we get:
Initial value =
210 x 100 x 100 / (100 − 12.5)(100 − 70)
=
210 x 100 x 100 / (87.5)(30)
= Rs 800
Hence, he had Rs 800 initially.

24. Prakash and chintu deposits Rs 1200 in a common fund. 20% of the initial amount is taken by Prakash and 40% of the remaining amount is taken by Chintu. How much is left in the common fund?
  A.  Rs 576
  B.  Rs 574
  C.  Rs 586
  D.  Rs 566
     
   
View Answer

Shortcut:
If initial quantity is Z and a% of the quantity is taken by the first, b% of the remaining is taken by the second and c% of the remaining is taken by the third person. Then
Z x (100 − a)(100 − b)(100 − c) / 100 x 100 x 100
left in the fund.
Here, Z = 1200, a = 20, b = 40
Using these value in shortcut, we get:
Left value =
1200 x (100 − 20)(100 − 40) / 100 x 100
=
1200 x 80 x 60 / 100 x 100
= Rs 576
Hence, left fund is Rs 576.

25. A man deposited 50% of the initial amount to his locker. And again after some time he deposited 20% of the increased amount. Now the amount becomes Rs 18,000. How much was the initial amount?
  A.  Rs 9,000
  B.  Rs 12,000
  C.  Rs 11,000
  D.  Rs 10,000
     
   
View Answer

Shortcut:
If a% of the quantity is added. Again b% of the increased quantity is added. Again c% of the increased quantity is added. Now, it becomes Z, then the initial amount was
Z x 100 x 100 x 100 / (100 + a)(100 + b)(100 + c)
.
Here, Z = 18000, a = 50, b = 20
Using these value in shortcut, we get:
Initial value =
18000 x 100 x 100 / (100 + 50)(100 + 20)
=
18000 x 100 x 100 / 150 x 120
=
18000 x 100 / 15 x 12
= 10000
Hence, initial amount was Rs 10,000.

26. A man has Rs 4800 in his locker two years ago. In the first year, he deposited 20% of the amount in his locker. In the second year, he deposited 25% of the increased amount in his locker. Find the amount at present in his locker.
  A.  Rs 7,600
  B.  Rs 7,200
  C.  Rs 7,400
  D.  Rs 6,200
     
   
View Answer

Shortcut:
If initial amount is Z and a% of the initial amount is added. Again b% of the increased quantity is added. Again c% of the increased quantity is added. Now, the final amount is
Z x (100 + a)(100 + b)(100 + c) / 100 x 100 x 100
.
Here, Z = 4800, a = 20, b = 25
Using these value in shortcut, we get:
Final value =
4800 x (100 + 20) x (100 + 25) / 100 x 100
=
4800 x 120 x 125 / 100 x 100
=
48 x 120 x 125 / 100
= 48 x 12 x 12.5 = 7200
Hence, Present amount is Rs 7200.

27. If the annual increase in the population of a town is 4% and the present number of people is 15,625, what will the population be in 3 years?
  A.  17,566
  B.  18,576
  C.  17,576
  D.  17,676
     
   
View Answer

Shortcut:
If the original population of a town is P, and the annual increse rate is r%, then the population in n years is shown by P
(
1 +
r / 100
)
n.
Here, P = 15625, r = 4, n = 3
Using these value in shortcut, we get:
= 15625
(
1 +
4 / 100
)
3 = 15625
(
1 +
1 / 25
)
3 = 15625
(
25 + 1 / 25
)
3 = 15625
(
26 / 25
)
3 = 15625
(
26 x 26 x 26 / 25 x 25 x 25
)
= 17576
Hence, population will be 17,576.

28. If the annual increase in the population of a town be 4% and the present population be 17576, What was it three years ago?
  A.  15,625
  B.  16,625
  C.  15,635
  D.  15,525
     
   
View Answer

Shortcut:
If the annual increase rate in the population is r% and the present population be P, then the population n years ago is given by
P /
(
1 +
r / 100
)
n

Here, P = 17576, r = 4, n = 3
Using these value in shortcut, we get:
Required population =
17576 / [1 + 4/100]3
=
17576 / [1 + 1/25]3
=
17576 / [(25 + 1)/25]3
=
17576 / 26/25 x 26/25 x 26/25
=
17576 x 25 x 25 x 25 / 26 x 26 x 26
= 25 x 25 x 25 = 15625
Hence, population was 15,625.

29. If the annual decrease in the population of a town is 5% and the present number of people is 40,000. What will the population be in 2 years?
  A.  36,200
  B.  36,100
  C.  35,100
  D.  36,150
     
   
View Answer

Shortcut:
If the original population of a town is P and the annual decrease rate of the population is r%, then the population in n years will be P
(
1 −
r / 100
)
n.
Here, P = 40000, r = 5, n = 2
Using these value in shortcut, we get:
= 40000
(
1 −
5 / 100
)
2 = 40000
(
1 −
1 / 20
)
2 = 40000
(
20 − 1 / 20
)
2 =
40000 x 19 x 19 / 20 x 20
= 1000 x 19 x 19 = 36100
Hence, population will be 36,100.

30. If the annual decrease in the population of a town be 4% and the present population be 57600, what was it two years ago?
  A.  62,400
  B.  63,500
  C.  62,500
  D.  62,600
     
   
View Answer

If the annual decrease rate in the population is r% and the present population be P, then the population n years ago is given by

P /
(
1 −
r / 100
)
n

Here, P = 57600, r = 4, n = 2
Using these value in shortcut, we get:
Required population =
57600 / [1 − 4/100]2
=
57600 / [1 − 1/25]2
=
57600 / [(25 − 1)/25]2
=
57600 / 24/25 x 24/25
=
57600 x 25 x 25 / 24 x 24
= 100 x 25 x 25 = 62500
Hence, population was 62,500.

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