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 $$y:z=5:3$$Â -------------(ii)
Multiplying equation (i) by 5 and equation (ii) by 7
=> $$x:y:z=25:35:21$$
Let $$x=25k$$, $$y=35k$$ and $$z=21k$$
=>Â 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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