Correct Answer - Option 3 : 4 : 5 : 6
Given:
Total Profit = Rs. 3000
X’s share is 400 less than Z
Y’s share is 200 less than Z
Calculation:
Let the share of Z be ‘a’
⇒ X’s share = a – 400
⇒ Y’s share = a – 200
According to the question,
⇒ X + Y + Z = 3000
⇒ a + (a – 200) + (a – 400) = 3000
⇒ 3a – 600 = 3000
⇒ 3a = 3000 + 600
⇒ 3a = 3600
⇒ a = 1200
Now shares will be,
⇒ X’s share = 1200 – 400 = 800
⇒ Y’s share = 1200 – 200 = 1000
⇒ Ratio of profit of X : Y : Z = 800 : 1000 : 1200
Simplifying ratio, we get
⇒ Ratio of profit of X : Y : Z = 4 : 5 : 6
∴ The ratio of share of profit of X, Y and Z is 4 : 5 : 6