a = x - 10 and b = y - 3

\(\frac{x}{b} = \frac{2}{3}\) and \(\frac{x}{y} = \frac{7}{12}\).

To find a/y

\(\frac{x}{b} = \frac{2}{3}\), therefore \(\frac{b}{x} = \frac{3}{2}\)

\(\frac{b}{x} * \frac{x}{y} = \frac{b}{y} = \frac{3}{2} * \frac{7}{12} = \frac{7}{8}\)

Therefore \(b = \frac{7y}{8}\)

Putting in b = y - 3, we get \(\frac{7y}{8} = y - 3\)

\(y - \frac{7y}{8} = \frac{y}{8} = 3\)

y = 24

Putting this in \(\frac{x}{y} = \frac{7}{12}\), we have \(\frac{x}{24} = \frac{7}{12}\)

x = 14

Therefore a = x - 10 = 14 - 10 = 4

a : y = 4 : 24 = 1 : 6


Option C

Arun Kumar
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a = x - 10
b = y - 3

x/b = 2/3
x/y = 7/12

a/y = x - 10 / y - 3 = ? <---Question


x = 2b /3 ---> 2b/3/ y = 7/12 ----> b = 21y / 24

21y/24 = y - 3
y = 24

b = 21y/24 <----plug y back in
b = 21

x - 10 / y - 3
= 2b/3 - 10 / b + 3
= 2(21)/3 - 10 / 21 + 3
= 4/24
= 1/6

Answer is C.
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Official Answer
The question provides ratios, so draw a ratio box for each ratio. The ratio values of x are 2 and 7, so x must be a multiple of 2 × 7 = 14. In the ratio box with x and b, use a multiplier of 7, yielding a value for b of 21. In the ratio box with x and y, use a multiplier of 2, yielding a value for y of 24. Now compare b and y against the condition in the problem that b is 3 less than y. 21 is 3 less than 24, so these values of b and y match the condition in the question. Now find the value of a. x is 14, and a is 10 less than x, so a is 14 – 10 = 4. The ratio of a to y is 4 to 24, which reduces to 1 to 6, or 1/6 .

The correct answer is choice C.