In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?

The correct option is 6 litres.

Let's solve the problem step-by-step to find out how much water needs to be added.

Step 1: Calculate the initial quantities of milk and water in the mixture.
The total volume of the mixture = 156 litres.
The initial ratio of milk to water = 7 : 6.

Total number of equal parts = 7 + 6 = 13 parts.

Value of 1 part = $\frac{156}{13}$ = 12 litres.

Initial quantity of milk = 7 × 12 = 84 litres.
Initial quantity of water = 6 × 12 = 72 litres.

Step 2: Set up the equation for adding water.
Let the quantity of water added be $x$ litres.
The quantity of milk remains unchanged at 84 litres.
The new quantity of water becomes (72 + $x$) litres.

According to the problem, the new ratio of milk to water is 14 : 13.

$\frac{84}{72+x}=\frac{14}{13}$

Step 3: Solve for $x$.
Cross-multiplying both sides:

$84\times 13=14\times (72+x)$

$1092=1008+14x$

Subtracting 1008 from both sides:

$14x=1092-1008$

$14x=84$

$x=\frac{84}{14}$

$x=6$

Therefore, 6 litres of water should be added to make the new ratio 14 : 13.