Q.9
Three friends, R, S and T shared toffee from a bowl.
R took 1/3rd of the toffees, but returned four to the bowl.
S took 1/4th of what was left but returned three toffees to the bowl.
T took half of the remainder but returned two back into the bowl.
If the bowl had 17 toffees left, how many toffees were originally there in the bowl?
Options:
(A) 38
(B) 31
(C) 48
(D) 41
Three Friends Sharing Toffees – Logical Word Problem
This problem involves fractional sharing and returning of toffees.
We solve it using the backward method to find the original number
of toffees in the bowl.
Step-by-Step Solution (Backward Method)
Step 1: After T’s Action
Let the number of toffees before T acted be x.
x − x/2 + 2 = 17
x/2 + 2 = 17
x/2 = 15 ⇒ x = 30
So, before T acted, there were 30 toffees.
Step 2: After S’s Action
Let the number of toffees before S acted be y.
y − y/4 + 3 = 30
3y/4 + 3 = 30
3y/4 = 27 ⇒ y = 36
So, before S acted, there were 36 toffees.
Step 3: After R’s Action
Let the original number of toffees be z.
z − z/3 + 4 = 36
2z/3 + 4 = 36
2z/3 = 32 ⇒ z = 48
Correct Answer
Option (C)
Original number of toffees = 48
Conclusion
Using the backward method, the only number that satisfies all
conditions is 48. Hence, option (C) is correct.
