Question

A mixture contains mango juice and water in the ratio 9 : 5 respectively. 28 litres of the mixture is replaced by water. Now the ratio of Mango juice and water became 18 : 17. Find the quantity of mango juice in the initial mixture.

Answer 1

The quantity of mango juice in the initial mixture is 90 liter

Given:

A mixture contains mango juice and water in the ratio 9 : 5 respectively

28 litres of the mixture is replaced by water.

The ratio of Mango juice and water became 18 : 17

To Find:

The quantity of mango juice in the initial mixture.

Solution:

Step 1:

Assume that inital mixture is 14x  litre

Mango Juice = 9x liter

Water = 5x liter

Step 2:

Find Mango juice in 28 liter

Mango Juice = (9x/14x) * 28  =  18 liter

Step 3:

Mango juice in Final mixture

Mango Juice = 9x -  18 liter

Water = 5x + 18 liter

Step 4:

Solve for x using given ratios

9x - 18 : 5x + 18 = 18 : 17

=> 17(9x - 18) = 18(5x + 18)

=> 153x - 306 = 90x + 324

=> 63x = 630

=> x = 10

Step 5:

Substitute x = 10  in 9x to find quantity of mango juice in the initial mixture

9x = 9(10) = 90 liter

Hence ,  the quantity of mango juice in the initial mixture is 90 liter