Discussion
The cost of painting the surface of a solid cuboid of dimensions 40 cm × 36 cm × x cm at ₹ 20 per 100 cm2 is ₹ 1,032. What is the value of x ?
Answer: B
The value of x is 15.
The cost is ₹ 20 per 100 square cm, so the area painted is:
\[ \begin{aligned} \text{Area} &= \frac{1032}{20} \times 100 = 5160 \\ 2(40 \times 36 + 36x + 40x) &= 5160 \\ 1440 + 76x &= 2580 \\ x &= \frac{1140}{76} = 15\ \text{cm} \end{aligned} \]
A check: 2(1440 + 540 + 600) = 5160 square cm, which costs 51.6 × 20 = ₹ 1,032. The other values give total surface areas of 5920 (x = 20), 6528 (x = 24) and 4704 (x = 12), none costing ₹ 1,032.
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