The ratio of 1/2sqrt(35) : 1/3sqrt(140) is equal to the ratio

Option d: 3:4. Solution: We need to find the ratio: R = frac{1/2sqrt(35)}{1/3sqrt(140)} First, simplify the term sqrt(140): sqrt(140) = sqrt(4 x 35) = sqrt(4) x sqrt(35) = 2sqrt(35) Substitute this value back into the ratio: R = frac{1/2sqrt(35)}{1/3 x 2sqrt(35)} Canceling the common factor sqrt(35) from both the numerator and the denominator: R = frac{1/2}{2/3} R = 1/2 x 3/2 = 3/4 Thus, the ratio is equal to 3:4. Hence, Option D is the correct answer.

Ratio, Proportion, Indices, LogarithmsPYQ Sept 25Question 4403 of 305

All Questions

The ratio of $\displaystyle \frac{1}{2}\sqrt{35} : \frac{1}{3}\sqrt{140}$ is equal to the ratio

Options

A4:3

B2:1

C5:4

D3:4

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Correct Answer

✅ Option d — 3:4

All Options:

A4:3
B2:1
C5:4
D3:4

Detailed Solution & Explanation

We need to find the ratio:

R = \frac{\frac{1}{2}\sqrt{35}}{\frac{1}{3}\sqrt{140}}

First, simplify the term

\displaystyle \sqrt{140}

\sqrt{140} = \sqrt{4 \times 35} = \sqrt{4} \times \sqrt{35} = 2\sqrt{35}

Substitute this value back into the ratio:

R = \frac{\frac{1}{2}\sqrt{35}}{\frac{1}{3} \times 2\sqrt{35}}

Canceling the common factor

\displaystyle \sqrt{35}

from both the numerator and the denominator:

R = \frac{\frac{1}{2}}{\frac{2}{3}}

R = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}

Thus, the ratio is equal to

\displaystyle 3:4

.
Hence, **Option D** is the correct answer.

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The ratio of 1235:13140\displaystyle \frac{1}{2}\sqrt{35} : \frac{1}{3}\sqrt{140}21​35​:31​140​ is equal to the ratio