Question

A 480 L mixture of milk and water in the ratio 5: 3 If 'X' L of the mixture is replaced by water and again '(X - 24)' L of the mixture is replaced by water. If the amount of water in the final mixture is 300 L, then find the value of 'X + 15'.

• A. 125
• B. 120
• C. 135
• D. 110

Answer 1

Answer: (C)

135

Answer 2

The correct option is (C): 135.
Milk = 480*$\frac{5}{8}$ = 300 L
Water = 480 - 300 = 180 L
Amount of milk in the mixture when 'X' L is replaced by water = 300 - X $\frac{5}{8}$ = (300 - $\frac{5x}{8}$)
Amount of water in the mixture when 'X' L is replaced by water = 180 - X $\frac{3}{8}$ + X = (180 + $\frac{5x}{8}$)
Amount of water in the mixture when 'X - 24' L is replaced by water =(180 + $\frac{5x}{8}$) - (X - 24) * $\frac{(180 + \frac{5X}{8})}{480}$+ (X - 24) = 300
If X = 125 - 15 = 110
The amount of water in the final mixture = (180 + 5 * $\frac{110}{8}$) - (110 -24) * $\frac{(180 + 5 * \frac{110}{8})}{480}$ + (110 - 24)
= $\frac{248.75 - (21392.5)}{480}$+ 86 [not satisfied]
If X = 120 - 15 = 105
The amount of water in the final mixture = (180 + 5 * $\frac{105}{8}$) - (105 -24) *$\frac{(180 + 5 * \frac{105}{8})}{480}$ + (105 - 24)
= 245.625 - 41.44 + 81 [Not satisfied]
If X = 135 - 15 = 120
The amount of water in the final mixture = (180 + 5 * $\frac{120}{8}$) - (120 -24) *$\frac{(180 + 5 * \frac{120}{8})}{480}$+ (120 - 24)
= 255 - 51 + 96
= 300 [satisfied].