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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% |

Important for :

1

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

A

Let the person C add c litres of water then18% of (240 + c) = c

82c = 240 × 18

C = | 2160 | litres = 52.68 litres approximately |

41 |

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

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

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

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

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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