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The ratio between the fourth proportional of 7, 5 and 3 to the third proportional of 7 and 13 is:
Question

The ratio between the fourth proportional of 7, 5 and 3 to the third proportional of 7 and 13 is:

A.

75 : 448

B.

15 : 169

C.

21 : 25

D.

25 : 21

Correct option is B

Formula Used:
Fourth proportional of a, b, c is bc/a
Third proportional to x, y is y2/x
Solution:

=>Fourth proportional to 7,5 and 3=5×37=157=>Third proportional of 7,13=1327Required ratio=1571327=15169=15 ⁣:169\Rightarrow \text{Fourth proportional to } 7, 5 \text{ and } 3 = \frac{5 \times 3}{7} = \frac{15}{7} \\ \Rightarrow \text{Third proportional of } 7, 13 = \frac{13^2}{7} \\ \therefore \text{Required ratio} = \frac{\frac{15}{7}}{\frac{132}{7}} = \frac{15}{169} = 15 \colon 169​​

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