A, B, C, and D are four friends living together in a flat and they have an agreement that whatever edible comes they will share equally among themselves. One day A's uncle came to him and gave a box of laddoos. Since no one was around, A divided the laddoos in four equal parts and ate his share after which he put the rest in the box. As he was closing the box, B walked in and took the box. He again divided remaining laddoos in four equal parts. A and B ate one part each and kept the remaining laddoos in the box. Suddenly C appeared and snatched the box. He again divided the laddoos in four equal parts, the three of them ate one part each and kept the remaining laddoos in the box. Later when D came, he again divided the laddoos in four equal parts and all four ate their respectively share. In total D ate 3 laddoos.
How many laddoos were given to A by his Uncle?
A, B, C, and D are four friends living together in a flat and they have an agreement that whatever edible comes they will share equally among themselves. One day A's uncle came to him and gave a box of laddoos. Since no one was around, A divided the laddoos in four equal parts and ate his share after which he put the rest in the box. As he was closing the box, B walked in and took the box. He again divided remaining laddoos in four equal parts. A and B ate one part each and kept the remaining laddoos in the box. Suddenly C appeared and snatched the box. He again divided the laddoos in four equal parts, the three of them ate one part each and kept the remaining laddoos in the box. Later when D came, he again divided the laddoos in four equal parts and all four ate their respectively share. In total D ate 3 laddoos.
How many laddoos were given to A by his Uncle?
The correct option is A 128
(a)
We will start solving this problem from the last line that D ate 3 laddoos.
Before D ate the laddoos there should be 3×4 = 12 laddoos.
Before C ate the laddoos there should be 12×3 + 12 = 48 laddoos.
Before B ate the laddoos, there should be 24×2 + 48 = 96 laddoos.
Before A ate laddoos, these should be 96×43=128 laddoos
At the Begining 128 laddoos
A
B
C
D
Remaining
A's share
B's share
C's share
D's share
32
24
12
3
24
12
3
12
3
96
48
12
0
71
39
15
3
(a)
We will start solving this problem from the last line that D ate 3 laddoos.
Before D ate the laddoos there should be 3×4 = 12 laddoos.
Before C ate the laddoos there should be 12×3 + 12 = 48 laddoos.
Before B ate the laddoos, there should be 24×2 + 48 = 96 laddoos.
Before A ate laddoos, these should be 96×43=128 laddoos
At the Begining 128 laddoos
| A | B | C | D | Remaining | |
| A's share B's share C's share D's share |
32 24 12 3 |
24 12 3 |
12 3 |
96 48 12 0 |
|
| 71 | 39 | 15 | 3 |
