Answer:
There were 16, 13 and 16 in first, second and third drawer respectively.
Explanation:
Given,
Total number of shirts = 45,
Number of drawers = 3,
Let x, y and z be the number in first, second and third drawer respectively,
After moving 6 shirts from the top drawer to the middle drawer,
Shirts in,
First drawer = x - 6
Second drawer = y + 6
Third drawer = z,
After moving 4 shirts from the middle drawer to the bottom drawer,
First drawer = x - 6
Second drawer = y + 6 - 4 = y + 2
Third drawer = z + 4,
Finally, after moving 5 shirts from the bottom drawer to the top drawer,
First drawer = x - 6 + 5 = x - 1,
Second drawer = y + 2
Third drawer = z + 4 - 5 = z - 1
According to the question,
x - 1 = y + 2 = z - 1
⇒ x - 1 = z - 1
⇒ x = z -----(1)
Also, x - 1 = y + 2
⇒ y = x - 1 - 2 = x - 3 ----(2)
Since, total shirts = 45
⇒ x + y + z = 45
From equation (1) and (2),
x + x - 3 + x = 45
⇒ 3x -3 = 45
⇒ 3x = 48
⇒ x = 16,
Again from equation (1) and (2),
z = 16 and y = 16 - 3 = 13
Hence, there were 16, 13 and 16 in first, second and third drawer respectively.
