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SSC CHSL 2024 PYQ — Question 68

SSC CHSL - 01 July 2024 - Shift 1 • Quantitative Aptitude • Q68

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The ratio of the diameters of two spheres is given as 1 : 4. The larger sphere is melted and 125 identical spheres are made out of the molten material. The smaller sphere is melted and 27 identical spheres are made out of the molten material. If the ratio of the volume of each of the 125 identical spheres to the volume of each of the 27 identical spheres is given as 1 : m, what is the value of m?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 1251728\frac{125}{1728}.

The ratio of the diameters of the two spheres is 1 : 4.

Since the volume of a sphere is proportional to the cube of its diameter, the ratio of the volumes of the two spheres is = 13:43=1:641^3 : 4^3 = 1 : 64 

Let the volume of the smaller sphere = X

Therefore, the volume of the larger sphere = 64X.

⇒ The smaller sphere is melted to create 27 identical spheres. Each of these spheres will have a volume =  X/27​.

⇒ The larger sphere is melted to create 125 identical spheres. Each of these spheres will have a volume = 64X/125​.

The ratio of the volume of each of the 125 identical spheres to the volume of each of the 27 identical spheres is

⇒ 1/m =  64X125x27\frac{\frac{64X}{125}}{\frac{x}{27}} 

⇒ 1/m = 64X125\frac{64X}{125} × 27X\frac{27}{X} 

⇒ 1/m = 1728125​\frac{1728}{125​}

Therefore, the ratio 1/m = 1728/125

Thus, m = 125/1728