To find the original fraction when the numerator is increased by 20% and the denominator is diminished by 10%, we can use the given equation and compute the original fraction.

Let the original fraction be p/q. Now, the equation have is:

(120% of p) / (90% of q) =16 / 21

Converting the percentages to decimals, we get:

(1.2p) / (0.9q) = / 21

Cross multiplying gives us:

21 * 1.2p =16 * 0.9q 25.2p = 14.4q 25.2p/q = 14.4

Dividing both sides by 25.2 gives us:

p/q = 14.4/25.2 /q = 4/7

Therefore, the original fraction is indeed 4/7, which matches the answer you provided.