Shortcut Trick
Total ratio parts = 5 + 7 + 8 = 20.
Since the additional amount is added in the same ratio, the ratio of the new total remains 5 : 7 : 8.
New total bonus = (4,34,000 ÷ 7) × 20 = 62,000 × 20 = ₹12,40,000.
Original total bonus = New total − Additional amount = 12,40,000 − 1,20,000 = ₹11,20,000.
∴ The correct answer is ₹11,20,000.
Alternate Method
Given:
Original Ratio = 5 : 7 : 8
Additional Bonus = ₹1,20,000
Final share of second department = ₹4,34,000
Formula Used: Share = (Individual Ratio / Sum of Ratios) × Total Amount
⇒ Total Ratio Parts = 5 + 7 + 8 = 20
⇒ New total bonus = (Individual Share × Total Parts) ÷ Individual Ratio Part
⇒ New total bonus = (4,34,000 × 20) ÷ 7
⇒ New total bonus = 62,000 × 20 = ₹12,40,000
⇒ Original total bonus = Final Total Bonus − Additional Bonus added
⇒ Original total bonus = 12,40,000 − 1,20,000
⇒ Original total bonus = ₹11,20,000
∴ The correct answer is ₹11,20,000.
Additional Information
Ratio Scaling Property
When a fixed amount is added to all parts of a ratio in the same proportion as the original ratio, the relative values remain unchanged, and the new total is simply the sum of the old total and the added amount.
Unitary Method in Ratios
If 'n' parts represent a value 'V', then 1 part represents V/n. The total value can be found by multiplying this single part value by the total number of parts in the ratio.
Ratio of Shares
Share of A : Share of B : Share of C = a : b : c. Total Amount = (Sum of Ratios × Share of A) ÷ a.