From a basket of mangoes, the king took 1/6, the queen took 1/5 of the remainder, the three chief princes to ¼, 1/3, and ½ of the successive remainders, respectively. the youngest child took the remaining 3 mangoes. how many mangoes were in the basket originally
Accepted Solution
A:
let x---------> quantity of mangoes that were in the basket originally
we know that the king took 1/6 (1/6)*x-------> remainder is (5/6)*x
the queen took 1/5 of the remainder (1/5)*(5/6)*x---> (1/6)*x----> remainder is (5/6-1/6)*x----> (4/6)*x
one chief princes to ¼ of the remainder (1/4)*(4/6)*x-----> (1/6)*x------> remainder is (4/6-1/6)*x----> (3/6)*x
second chief princes to 1/3 of the remainder (1/3)*(3/6)*x-----> (1/6)*x-------> remainder is (3/6-1/6)*x----> (2/6)*x
third chief princes to 1/2 of the remainder (1/2)*(2/6)*x-----> (1/6)*x--------> remainder is (2/6-1/6)*x----> (1/6)*x
we know the remaining is 3 mangoes so (1/6)*x=3-------> x=6*3------> x=18 mangoes