Question : The sum of the three numbers is 540. The ratio of second to third is 9 : 13 and that of first to third is 2 : 7. The third number is:
Option 1: 273
Option 2: 280
Option 3: 250
Option 4: 286
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Correct Answer: 273
Solution :
The ratio of 2nd : 3rd = 9 : 13
And the ratio of 1st : 3rd = 2:7
3rd number is common in both ratios, so to make the value equal, we need to multiply by 7 in 9 : 13 and by 13 in 2 : 7.
We get 1st : 2nd : 3rd = 26 : 63 : 91
Let the 1st, 2nd and 3rd number be 26x, 63x, and 91x.
According to the question,
26x + 63x + 91x = 540
⇒ 180x = 540
$\therefore$ x = 3
Thus, the 3rd number = (91 × 3) = 273
Hence, the correct answer is 273.
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