The ratio of the difference obtained by subtracting 2 from thrice a number to the sum of twice the same number and 5 is 13 : 15. What is the number?

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Solution

Let the number be x.
The ratio of the difference obtained by subtracting 2 from thrice the number to the sum of twice the same number and 5 is 13 : 15. That is
$\frac{3 x - 2}{2 x + 5} = \frac{13}{15}$
⇒ 15(3x − 2) = 13(2x + 5)
⇒ 45x − 30 = 26x + 65
⇒ 19x = 95
∴ x = 5
∴ The number is 5.

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The ratio of the difference obtained by subtracting 2 from thrice a number to the sum of twice the same number and 5 is 13 : 15. What is the number?

Let the number be x. The ratio of the difference obtained by subtracting 2 from thrice the number to the sum of twice the same number and 5 is 13 : 15. That is 3x-22x+5=1315 ⇒ 15(3x − 2) = 13(2x + 5) ⇒ 45x − 30 = 26x + 65 ⇒ 19x = 95 ∴ x = 5 ∴ The number is 5.