Question 98

x is greater than y by 12 and the respective ratio, between x and y is 3 : 2. What is the sum of a third number z and x, if z is 1/3 of y ?

Solution

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x is greater than y by 12 and the respective ratio, between x and y is 3 : 2

=> $$x - y = 12$$ => $$x = 12 + y$$

Also, $$\frac{x}{y} = \frac{3}{2}$$

=> $$\frac{12 + y}{y} = \frac{3}{2}$$

=> $$24 + 2y = 3y$$

=> $$3y - 2y = y = 24$$

=> $$x = 12 + 24 = 36$$

Now, $$z = \frac{1}{3} \times y$$

=> $$z = \frac{1}{3} \times 24 = 8$$

$$\therefore z + x = 8 + 36 = 44$$

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