Question 8

Of three positive numbers, the ratio of first and second is 5: 2, ratio of second and third is 5: 4. The product of first and third is 1800. What is the sum of the three numbers?

Solution

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

Thus, $$x:y=5:2$$ -----------(i)

and $$y:z=5:4$$ -------------(ii)

Multiplying equation (i) by 5 and equation (ii) by 2

=> $$x:y:z=25:10:8$$

Let $$x=25k$$, $$y=10k$$ and $$z=8k$$

=> Product = $$25k\times8k=1800$$

=> $$k^2=\frac{1800}{200}=9$$

=> $$k=\sqrt9=3$$

$$\therefore$$ Sum of three numbers = $$25k+10k+8k=43k$$

= $$43\times3=129$$

=> Ans - (D)

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