Question
Download Solution PDFTwo numbers are in the ratio 4 : 5. If 17 is subtracted from each, the new numbers are in the ratio 11 : 14. If 20 is added to each of the original numbers, then the ratio becomes:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two numbers are in the ratio 4:5. If 17 is subtracted from each, the new numbers are in the ratio 11:14.
Formula used:
Let the two numbers be 4x and 5x.
Calculation:
After subtracting 17 from each, the new numbers become (4x - 17) and (5x - 17).
Given the new ratio: (4x - 17) / (5x - 17) = 11 / 14
⇒ 14(4x - 17) = 11(5x - 17)
⇒ 56x - 238 = 55x - 187
⇒ 56x - 55x = 238 - 187
⇒ x = 51
Original numbers are 4x = 4×51 = 204 and 5x = 5×51 = 255.
After adding 20 to each of the original numbers:
New numbers are 204 + 20 = 224 and 255 + 20 = 275.
New ratio: 224 : 275
∴ The correct answer is option (1).
Last updated on Jul 15, 2025
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