Question 8

The sum of three numbers is 162. If the ratio of the first number to the second number is 5: 7 and that of the second number to the third number is 5: 3, then what is the second number?


Let the numbers be $$x,y,z$$

Thus, $$x:y=5:7$$ -----------(i)

and $$y:z=5:3$$ -------------(ii)

Multiplying equation (i) by 5 and equation (ii) by 7

=> $$x:y:z=25:35:21$$

Let $$x=25k$$, $$y=35k$$ and $$z=21k$$

=> Sum of three numbers = $$25k+35k+21k=81k=162$$

=> $$k=\frac{162}{81}=2$$

$$\therefore$$ Second number = $$35\times2=70$$

=> Ans - (B)

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