New Pattern Data Interpretation for SBI PO, IBPS PO, IBPS RRB PO, IBPS Clerk, SBI Clerk | DI Based on Mixture and Alligation

Directions : Study the following table chart carefully and answer the questions given beside.

Ram has 5000 litres of pure milk. He sells 40% of the total milk to six different persons(A,B,C,D,E,F) and the remaining 60% of total milk he utilizes in his own shop. Each person, A, B, C, D, E, and F mixes water in pure milk. The following table given below shows the sales of milk to six different persons by Ram as a percentage of total sales and it also shows the concentration of water after adding water in pure milk by each of the six persons.

Person Sales of Milk The concentration of water (After adding water in pure milk)
A 24% 24%
B 10% 10%
C 12% 18%
D 7% 15%
E 28% 25%
F 19% 12%
1
What is the difference between the total quantity of water added by Person A and that of Person C? (approximately) 
» Explain it
B
40% of 5000 = 2000 litres Ram sells to six persons 

Person Sales of Milk The concentration of water (After adding water in pure milk)
A 24% of 2000 = 480 litres 24%
B 10% of 2000 = 200 litres 10%
C 12% of 2000 = 240 litres 18%
D 7% of 2000 = 140 litres 15%
E 28% of 2000 = 560 litres 25%
F 19% of 2000 = 380 litres 12%

Let Person A add ‘a’ litres of water then the total quantity of solution = 480 + ‘a’ litres, in which the concentration of water is 24% 
 
Therefore, 24% of (480 + a) = a 
 
100a = 24 × 480 + 24a 
 
76a = 24 × 480
 
A = 2880/19 litres = approximately 151.58 litres = Quantity of water added by Person A 
 
Similarly, Let the person C add c litres of water then 
 
18% of (240 + c) = c 
 
82c = 240 × 18 
 
C =  2160  litres = 52.68 litres approximately = quantity of water added by person C
41

The required difference = 151.58 – 52.68 = 98.9 litres = approximately 99 litres 

Hence, option B is correct.
 
2
What is the respective ratio of the total quantity of water added by Person C and the total quantity of water added by Person E?
» Explain it
A
Let the person C add c litres of water then

18% of (240 + c) = c

82c = 240 × 18

C =  2160  litres = 52.68 litres approximately
41
= quantity of water added by person C
Let the person E add e litres of water

Then, 25% of (560 + e) = e

75e = 560 × 25
 
E =  560  litres = quantity of water added by person E
3

Reqd. ratio =  2160  :  560  = 81 : 287
41 3

Hence, option A is correct.
3
Who among the following added least quantity (In litres) of water in pure milk?A
» Explain it
B
Let Person A add ‘a’ litres of water then the total quantity of solution = 480 + ‘a’ litres, in which the concentration of water is 24%

Therefore, 24% of (480 + a) = a

100a = 24 × 480 + 24a

76a = 24 × 480
 
a =  2380  litres = approximately 151.58 litres
19

= Quantity of water added by Person A

Let the person B add b litres of water then,

10% of (200 + b) = b

b = quantity of water added by Person B
200  litres = approximately 22.22 litres
9

Let the person C add c litres of water then

18% of (240 + c) = c

82c = 240 × 18
C =  2160  litres = 52.68 litres approximately
41

= quantity of water added by person C
Let the person D add d litres of water

15% of (140 + d) = d
d =  140 × 15  = 24.70 litres
85

= quantity of water added by person D
Let the person E add e litres of water

Then, 25% of (560 + e) = e

75e = 560 × 25
 
E =  560  litres = 186.67 litres approximately
3

= quantity of water added by person E
Let the person F add f litres of water then,

12% of (380 + f) = f

88f = 380 × 12

f = 51.82 litres = quantity of water added by person F

therefore, B added least quantity (In litres) of water

Hence, option B is correct.
4
Suppose, A, B, and C mix their solutions in one can then what would be the concentration of milk in the new solutions? (approximately) 
» Explain it
C
Person Sales of Milk The concentration of water (After adding water in pure milk)
A 24% of 2000 = 480 litres 24% = 151.58 litres
B 10% of 2000 = 200 litres 10% = 22.22 litres
C 12% of 2000 = 240 litres 18% = 52.56 litres

When A, B, and C mix their solution in one can then the quantity of milk in the new solution = 480 + 200 + 240 = 920 litres 
 
And the quantity of milk in the new mixture = 151.58 + 22.22 + 52.56 = 226.36 litres 
 
The total quantity of new solution = 920 + 226.36 = 1146.36 litres 
 
The required concentration of milk in the new solution

920 × 100  = 80.25% approximately
1146.36

Hence, option C is correct.
5
How many total litres of water was added by all the persons together? (approximately) 
» Explain it
D
Person Sales of Milk The concentration of water (After adding water in pure milk)
A 24% of 2000 = 480 litres 24% = 151.58 litres
B 10% of 2000 = 200 litres 10% = 22.22 litres
C 12% of 2000 = 240 litres 18% = 52.68 litres
D 7% of 2000 = 140 litres 15% = 24.70 litres
E 28% of 2000 = 560 litres 25% = 186.67 litres
F 19% of 2000 = 380 litres 12% = 51.82 litres

The total quantity of water added by all the persons together = 151.58 + 22.22 + 52.68 +24.70 + 186.67 + 51.82 = approximately 489.67 litres = approximately 490 litres 

Hence, option D is correct.

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