£) There are 120 mangoes in a basket and 168 mangoes in another basket.
Find the greatest number of mangoes which are to be taken out at a time
from each basket so that both of them will be emptied simultaneously.

The greatest number of mangoes which are to be taken out at a time from each basket so that both of them emptied simultaneously is the number of mangoes in each basket which is 120 mangoes for one basket and 168 mangoes for the other basket

Explanation:

Given that the number of mangoes in one basket = 120 mangoes

Also, the number of mangoes in another basket = 168 mangoes

The greatest number of mangoes, X and Y that are to taken out from each basket so that both of them will empty simultaneously is found as follows;

We note that the ratio of the number of mangoes in both baskets are;

120:168 = 5:7

Therefore, we have;

5 × Y = 120

Y = 20/5 = 24

Similarly, we have;

7 × X = 168

X = 168/7 = 24

We can take 5 mangoes from one basket and 7 mangoes from the other basket 24 times, for both mangoes to empty the same time

We can also take 5×12 = 60 mangoes twice from one basket and 7 × 12 = 84 mangoes twice from the other basket to empty the baskets

We can also take 120 mangoes one from one basket and 168 mangoes one from the other basket to empty the baskets.

Therefore, the greatest number of mangoes which are to be taken out at a time from each basket so that both of them emptied simultaneously is the number of mangoes in each basket which is 120 mangoes for one basket and 168 mangoes for the other basket.