Question

If y is directly proportional to x, then find a and b

x	6	12	18	a
y	5	10	15	b

• A. a = 24, b = 20
• B. a = 20, b = 24
• C. a = 30, b = 20
• D. a = 30, b = 25

Answer 1

The correct option is A a = 24, b = 20

From the table we observe as x increases, y also increases such that the ratio of x and y remains the same
$\frac{x}{y}=\frac{6}{5}$
As the fractions are equivalent,

$\Rightarrow \frac{12}{10}=\frac{2\times 6}{2\times 5}=\frac{6}{5}$
If we multiply with 2 on both the numerator and the denomiantor in the fraction $\frac{6}{5}$, we get $\frac{12}{10}$

$\Rightarrow \frac{18}{15}=\frac{3\times 6}{3\times 5}=\frac{6}{5}$
If we multiply with 3 on both the numerator and the denomiantor in the fraction $\frac{6}{5}$, we get $\frac{18}{15}$


Similarly, the next number to be multiplied with the fraction $\frac{6}{5}$is 4,
$\Rightarrow \frac{6}{5}=\frac{4\times 6}{4\times 5}=\frac{24}{20}$

Hence, a = 24, b = 20