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SSC GD 2024 PYQ — Question 54

SSC GD Const (English) - 24 Feb 2024 - Shift 1 • Quantitative Aptitude • Q54

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The cost of diamond is directly proportional to the square of its weight. The cost of diamond is Rs. 87880. It brak into two pieces whose weight are in the ratio of 5 : 8. What is the loss incurred because of the breakage?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. Rs. 41600.

The weight of the diamond  = ( w )

⇒ C = k × w2

⇒ C=k⋅w2=87880C = k \cdot w^2 = 87880

⇒ (w1) (w2) = (5) / (8)

⇒ w1 = 513⋅w\frac{5}{13} \cdot w \quad and  w2 = 813⋅w\frac{8}{13} \cdot w

The cost of the first piece (weight ( w1)) is:

C1 = k⋅w12=k⋅(513⋅w)2=k⋅25169⋅w2k \cdot w_1^2 = k \cdot \left( \frac{5}{13} \cdot w \right)^2 = k \cdot \frac{25}{169} \cdot w^2

The cost of the second piece (weight ( w2)) is:

⇒C2=k⋅w22=k⋅(813⋅w)2=k⋅64169⋅w2C_2 = k \cdot w_2^2 = k \cdot \left( \frac{8}{13} \cdot w \right)^2 = k \cdot \frac{64}{169} \cdot w^2

the total cost of the broken pieces is:

⇒ C1+C2=k⋅25169⋅w2+k⋅64169⋅w2=k⋅89169⋅w2C_1 + C_2 = k \cdot \frac{25}{169} \cdot w^2 + k \cdot \frac{64}{169} \cdot w^2 = k \cdot \frac{89}{169} \cdot w^2

Loss = Original cost -  Cost of broken pieces = 87880−(k⋅89169⋅w2)87880 - \left( k \cdot \frac{89}{169} \cdot w^2 \right)

Loss = 87880−87880⋅89169=87880⋅(1−89169)87880 - 87880 \cdot \frac{89}{169} = 87880 \cdot \left( 1 - \frac{89}{169} \right)

Loss = 87880⋅8016987880 \cdot \frac{80}{169}

Loss = 87880×80169=7030400169≈41600\frac{87880 \times 80}{169} = \frac{7030400}{169} \approx 41600

The loss incurred because of the breakage is approximately Rs. 41,600.