MATH SOLVE

2 months ago

Q:
# 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

the answer is

18 mangoes

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

the answer is

18 mangoes