Correct Answer - Option 1 : 100, 120
Given:
The ratio of original number = 5 ∶ 6
New 1st number = 165% of original 1st number
New 2nd number = 140% of the original 2nd number
Sum of the new number = 333
Calculation:
Let the original number be 5x and 6x.
New 1st number = 165% of 5x
New 2nd number = 140% of 6x
Sum of the new number = 333
⇒ 165% of 5x + 140% of 6x = 333
⇒ 825x/100 + 840x/100 = 333
⇒ 8.25x + 8.4x = 333
⇒ 16.65x = 333
⇒ x = 333/16.65
⇒ x = 20
Original 1st number = 5x
⇒ Original 1st number = 100
Original 2nd number = 6x
⇒ Original 2nd number = 120
∴ The original numbers are 100 and 120.