Question

A can is full of a mixture of two liquids a and b in the ratio of 7:5 when 9 litres of mixture are drawn off from the can and replaced by the same quantity of liquid b the ratio of a and b in the can becomes 7:9 the capacity of the can is

Answer 1

Ratio of liquids (a:b) = 7:5
Let the quantity of a = 7x && b = 5x
Total = 12x

Now, 9 L of the mixture was removed:
Hence, a = 7/12 * (12x - 9)
b = 5/12 * (12x -9)

Now, 9 L of b was added
b = 5/12 *(12x -9 ) + 9
The new ratio (a:b) = 7:9
[7/12*(12x-9)]/[5/12 *(12x -9 ) + 9] = 7/9
[(84x -  63)/12] / [(60x - 45 + 9*12)/12] = 7/9
[84x - 63]/[60x + 63] = 7/9
9*[84x - 63] = 7*[60x + 63]
756x - 567 = 420x + 441
756x - 420x = 441 + 567
336x = 1008
x = 3
Hence the capacity of can(a;b=7:5) = 12 x = 12*3 = 36 L
Hope it helps.