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SSC MTS 2024 PYQ — Question 6

SSC MTS - 30/10/2024 - (9:00 AM - 11:00 AM) • Quantitative Aptitude • Q6

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The weight of a sphere is jointly proportional to the cube of its radius and the density of the material of which it is made. The radii of two spheres are 17 : 8 and the densities of materials 3 : 4. If the weight of the second sphere be 40 kg, then the approximate weight of the first sphere is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 287.87 kg.

Given, W = kr3d

Now, for two balls, ratio of weights, W1W2=r13d1r23d2\frac{W_1}{W_2} = \frac{r_1^3 d_1}{r_2^3 d_2}

⇒ 40W2=173×383×4\frac{40}{W_2} = \frac{17^3 \times 3}{8^3 \times 4}

⇒ 40W2=147392048\frac{40}{W_2} = \frac{14739}{2048}

⇒ W2 = 40 × 7.2

⇒ W2 = 288 kg