The sum of three numbers is 100. The ratio of the first number to the second number is 4 : 9 and the ratio of the second to the third number is 3 : 4. Find the second number.
let the first no be A, second no be B and third no. CÂ
$$\frac{A}{B} = \frac{4}{9}$$
$$\frac{B}{C} = \frac{3}{4}$$
B is common in both so we have to balance the B
$$\frac{A}{B} = \frac{4\times 3}{9\times 3}$$
$$\frac{B}{C} = \frac{3\times 9}{4\times 9}$$
$$\frac{A}{B} = \frac{12}{27}$$
$$\frac{B}{C} = \frac{27}{36}$$
so
12x + 27x + 36x = 100
75x = 100
x = $$\frac{4}{3}$$
so,second no =Â 27x = 36
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