Question

? In what ratio must one add water to milk so as to gain 16.666% on selling this mixture at the cost price?​

Answer 1

Answer:

Let the cost price of 1 liter of milk = Rs.1

According to the question, cost price of milk is equal to the selling price of mixture (mixture of milk and water)

Hence the selling price of 1 liter of mixture = Rs.1

Gain = 16%

Hence the cost price of mixture = 100100+gain%×SP

( Here SP means selling price )

=100100+16×1

=100116=2529rs.

By the rule of mixture and alligation,

Cost price of 1 liter of water, c = 0

Cost price of 1 liter of milk, d = 1

Mean price, m = cost price of mixture =2529

Hence, d-m = 1−2529=29−2529=429

And m-c = 2529−0=2529

Therefore the ratio of water and milk in the mixture is,

d-m : m-c

=429:2529

As the denominator of both the terms are equal, hence the ratio is 4:25.

Therefore, in a 4:25 ratio water must be mixed with milk to gain 16% on selling the mixture at cost price.

So, the correct answer is “Option B”.

Note: You might get confused because the selling price of the mixture is equal to the cost price of the milk as it is trickily mentioned in the question.

We can also solve this by using alternative methods.

Alternative method- Let the amount of water mixed is x liter

CP of milk = SP of mixture = 1(let)

Actual CP of mixture is 100/116

By adding water we get profit 16/116

Therefore for every 100 liter of milk, 16 liter of water is added.

Hence the ratio of water and milk in the mixture is 16/100 = 4/25 = 4:25

Answer 2

Answer:

The ratio of milk to water should be 6:1 so as to gain 16.666% on selling this mixture at the cost price.

Step-by-step explanation:

• Convert the profit percentage into the fraction -

           Percentage into Fraction

         ⇒ 16.667% = $\frac{1}{6}X100$           -----------------------------Eq.1

• The profit percentage formula = $\frac{sale price - cost price}{cost price} X 100$

Corresponding the Eq.1 value to the profit percentage formula.

We get sale price = 7 and cost price = 6, but according to the question, both cost price and sale price are equal.

Therefore, The profitability of the 16.667% can only be achieved by adding water to the milk.

Hence, adding 1 litre of water to every 6 litres of Milk will give us the desired profitability.

Hypothetical situation -

Let the Milk vendor has 6 litres of milk costing Rs.1 for each litre. So by adding one litre of water into 6 litres of milk we get a total quantity of  7 litres.

Since water is free of cost, so our Total cost will be (6 x 1) = Rs. 6 and Total sales will be 7 x 1 = Rs. 7.

Calculating the profit we get,

= $(\frac{7 - 6}{6})X100$ = 16.66%

Hence the desired ratio of milk to water will be 6:1.

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