Home ≫ Arithmetic Aptitute ≫ Alligation ≫ Page 1
1. In what proportion must rice at Rs 3.10 per kg be mixed with rice at Rs 3.60 per kg, so that the mixture be worth of Rs 3.25 per kg?
  A.  3:7
  B.  7:3
  C.  4:3
  D.  3:4
     
   
View Answer

Shortcut:
The proportion in which rice at Rs 'a' per kg must be mixed with rice at Rs 'b' per kg, so that the mixture be worth Rs 'c' per kg, is given by
b − c / c − a

Here, a = 3.10, b = 3.60, c = 3.25
Using these values in the shortcut, we get:
Required ratio =
3.60 − 3.25 / 3.25 − 3.10
=
0.35 / 0.15
=
35 / 15
=
7 / 3

Hence, the required ratio is 7 : 3.

2. In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg so that by selling the mixture at 63 paise per kg he may gain
1 / 6
of his outlay?
  A.  1:3
  B.  3:1
  C.  2:3
  D.  None of the above
     
   
View Answer

Shortcut:
The proportion in which rice at Rs 'a' per kg must be mixed with rice at Rs 'b' per kg, so that the mixture be worth Rs 'c' per kg, is given by
b − c / c − a

1 +
1 / 6
=
7 / 6
of the cost price of a kg of the mixture = 63 paise
∴ cost price of a kg of the mixture =
63 / 7/6
= 54 paise
Here, a = 0.48, b = 0.72, c = 0.54
Using these values in the shortcut, we get:
Required ratio =
.72 − 0.54 / 0.54 − 0.48
=
0.18 / 0.06
=
6 / 18
=
1 / 3

Hence, the required ratio is 1 : 3.

3. Sugar at Rs 15 per kg is mixed with sugar at Rs 20 per kg in the ratio 2:3. Find the price per kg of the mixture.
  A.  Rs 19 per kg
  B.  Rs 16 per kg
  C.  Rs 20 per kg
  D.  Rs 18 per kg
     
   
View Answer

Shortcut:
The proportion in which rice at Rs 'a' per kg must be mixed with rice at Rs 'b' per kg, so that the mixture be worth Rs 'c' per kg, is given by
b − c / c − a

Here, a = 15, b = 20, c = ?
Using these values in the shortcut, we get:
2 / 3
=
20 − c / c − 15

2 / 3
=
20 − c / c − 15

2 x (c − 15) = 3(20 − c)
2c − 30 = 60 − 3c
2c + 3c = 60 + 30
5c = 90
c =
90 / 5
= 18
Hence, the required rate is Rs 18 per kg.

4. A grocer buys cheap tea at Rs 5.25 per kg and quality tea at Rs 7.50 per kg. How must he mix them so that by selling the mixture at Rs 7 per kg he may gain
1 / 6
of his outlay.
  A.  3 : 1
  B.  1 : 2
  C.  6 : 5
  D.  2 : 1
     
   
View Answer

Shortcut:
The proportion in which rice at Rs 'a' per kg must be mixed with rice at Rs 'b' per kg, so that the mixture be worth Rs 'c' per kg, is given by
b − c / c − a

1 +
1 / 6
=
7 / 6
of the cost price of a kg of the mixture = 7
∴ cost price of a kg of the mixture =
7 / 7/6
= 6
Here, a = 5.25, b = 7.50, c = 6
Using these values in the shortcut, we get:
Required ratio =
7.50 − 6 / 6 − 5.25
=
1.50 / 1.25
=
150 / 125
=
6 / 5
= 6 : 5
Hence, the required ratio is 6 : 5.

5. In what proportion should water and milk at Rs 22.50 a litre be mixed to reduce the price to Rs 18 per litre?
  A.  3:4
  B.  1:4
  C.  5:4
  D.  4:1
     
   
View Answer

Required proportion =
20.50 − 18 / 18 − 0
[∴ water worths Rs 0 per litre]
=
4.50 / 18
= 1 : 4

6. pulses at Rs 50 per kg are mixed with pulses of Rs 90 per kg to make a mixture of 17 kg worth Rs 70 per kg, how many kilograms of each are taken?
  A.  8
1 / 2
kg, 8
1 / 2
kg
  B.  8 kg, 9 kg
  C.  9 kg, 8 kg
  D.  11 kg, 6 kg
     
   
View Answer

Required proportion =
90 − 70 / 70 − 50

=
20 / 20
= 1 : 1
Hence,
17 / 1 + 1
= 8
1 / 2
kg of each are taken.

7. A person bought 60 quiltals of rice of two different sorts for Rs 4642.50. The good quality costs Rs 80 per quintal and the cheap of Rs 75.5 per quintal.How many quintals were there of each sort?
  A.  Good quality:35 quintals, Cheap quality:25 quintals
  B.  Good quality:24 quintals, Cheap quality:36 quintals
  C.  Good quality:25 quintals, Cheap quality:35 quintals
  D.  None of the above
     
   
View Answer

Per quintal cost of two different sorts of rice =
4642.5 / 60
= Rs 77.375 per quintal
Proportion =
75.50 − 77.375 / 77.375 − 80
=
1.875 / 2.625
= 5 : 7
The quantity of good sort =
60 / 12
x 5 = 25 quintals
The quantity of cheap sort =
60 / 12
x 7 = 35 quintals.

8. A man has whisky worth Rs 22 per litre and another lot worth Rs 18 per litre. Equal quantities of these are mixed with water to obtain a mixture of 50 litres worth Rs 16 per litre. Find how much water the mixture contains?
  A.  18 litres
  B.  8 litres
  C.  12 litres
  D.  10 litres
     
   
View Answer

Two lots of whisky having equal quantities are mixed.
Let the price of mixutre of whisky be Rs x per litre.
18 − x / x − 22
= 1
∴ x = Rs 20 per litre
Now this mixture is mixed with water and worth Rs 16 per litre.
Hence, the proportion of water to mixture =
20 − 16 / 16 − 0
= 1 : 4
∴ quantity of water =
50 / 1 + 4
x 1 = 10 litres.

9. How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg, so that he may, on selling the mixture at 40 paise per kg, gain 25% on the outlay?
  A.  25 kg
  B.  20 kg
  C.  22 kg
  D.  18 kg
     
   
View Answer

Shortcut:
The quantity of salt at Rs 'a' per kg that a man must mix with 'm' kg of salt at Rs 'b' per kg, so that he may, on selling the mixture at Rs 'c' per kg, gain 'g%' on the outlay is given by
100c − b(100 + g) / a(100 + g) − 100c
x m
Here, a = 42, b = 24, c = 40, g = 25, m = 25
Using these values in the shortcut, we get:
Required answer =
100 x 40 − 24(100 + 25) / 42(100 + 25) − 100 x 40
x 25
=
4000 − 24 x 125 / 42(125) − 4000
x 25
=
4000 − 3000 / 5250 − 4000
x 25
=
1000 / 1250
x 25 = 20 kg

10. Suresh purchased 25 kg of rice at the rate of Rs 16.50 per kg and 35 kg of rice at the rate of Rs 25.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make 25% profit?
  A.  Rs 26.50
  B.  Rs 26
  C.  Rs 20.50
  D.  Rs 24.50
     
   
View Answer

Shortcut:
The quantity of salt at Rs 'a' per kg that a man must mix with 'm' kg of salt at Rs 'b' per kg, so that he may, on selling the mixture at Rs 'c' per kg, gain 'g%' on the outlay is given by
100c − b(100 + g) / a(100 + g) − 100c
x m
Note: If we suppose that the quantity of salt at Rs a per kg is n, then
n =
100c − b(100 + g) / a(100 + g) − 100c
x m
Here, a = 16.50, b = 24.5, c = ?, g = 25, n = 25, m = 35
Using these values in the shortcut, we get:
25 =
100 x c − 24.50(100 + 25) / 16.50(100 + 25) − 100 x c
x 35
25 =
100c − 24.50 x 125 / 16.50 x 125 − 100c
x 35
25 =
100c − 3062.5 / 2062.5 − 100c
x 35
25(2062.5 − 100c) = (100c − 3062.5)35
5(2062.5 − 100c) = (100c − 3062.5)7
10312.5 − 500c = 700c − 21437.50
1200c = 31750
∴ c =
31750 / 1200
= 26.458 or 26.50
Hence, the should the mixture at Rs 26.50 per kg.

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .