The cost of three cricket balls equals the cost of two pairs of leg pads; the cost of three pairs of leg pads equals the cost of two pairs of gloves, and the cost of three pairs of gloves equals the cost of two cricket bats; if one cricket bat costs Rs. 54, what is the cost of one cricket ball?

Introduction / Context:
This question presents a chain of proportional cost relationships between cricket balls, leg pads, gloves and bats. By expressing everything in terms of one variable and using the known cost of a bat, we can work backward to find the cost of a single ball. It is a typical algebraic application of ratios and proportionality used in aptitude examinations.

Given Data / Assumptions:

• Cost of 3 cricket balls equals the cost of 2 pairs of leg pads.
• Cost of 3 pairs of leg pads equals the cost of 2 pairs of gloves.
• Cost of 3 pairs of gloves equals the cost of 2 cricket bats.
• Cost of 1 cricket bat = Rs. 54.
• We are asked to find the cost of 1 cricket ball.

Concept / Approach:
Let the cost of one cricket ball be B, cost of one pair of leg pads be L, cost of one pair of gloves be G, and cost of one bat be T. The given relationships can be written as linear equations: 3B = 2L, 3L = 2G, and 3G = 2T. We also know T = 54. By solving this chain stepwise, we can express B in terms of T and thus compute its numerical value. This approach uses simple algebra and careful substitution.

Step-by-Step Solution:
Step 1: Define variables as follows: B = cost of one ball, L = cost of one pair of leg pads, G = cost of one pair of gloves, T = cost of one bat.Step 2: From the problem, cost of 3 balls equals cost of 2 pairs of leg pads: 3B = 2L.Step 3: Thus, L = (3 / 2) * B.Step 4: Cost of 3 pairs of leg pads equals cost of 2 pairs of gloves: 3L = 2G.Step 5: Substitute L into 3L = 2G: 3 * (3 / 2) * B = 2G.Step 6: This simplifies to (9 / 2) * B = 2G, so G = (9 / 4) * B.Step 7: Cost of 3 pairs of gloves equals cost of 2 bats: 3G = 2T.Step 8: Substitute G: 3 * (9 / 4) * B = 2T.Step 9: This gives (27 / 4) * B = 2T.Step 10: So B = (2T * 4) / 27 = (8T) / 27.Step 11: Given T = 54, substitute: B = (8 * 54) / 27.Step 12: Compute (8 * 54) / 27 = 8 * (54 / 27) = 8 * 2 = Rs. 16.

Verification / Alternative check:
We can verify by computing the costs up the chain. If one ball costs Rs. 16, then three balls cost 3 * 16 = Rs. 48. So two pairs of leg pads cost Rs. 48 and one pair costs 24. Then three pairs of leg pads cost 3 * 24 = Rs. 72, which equals cost of two pairs of gloves. So one pair of gloves costs 36. Three pairs of gloves cost 3 * 36 = Rs. 108, which should equal the cost of two bats, so each bat costs 108 / 2 = Rs. 54, exactly as given. The relationships are all satisfied, confirming our calculations.

Why Other Options Are Wrong:

• Rs. 12, Rs. 14, Rs. 18: None of these values produce a consistent chain with the given relations when propagated to the bat cost of Rs. 54. They all lead to mismatch at some step.

Common Pitfalls:

• Inverting ratios incorrectly, for example writing 2L = 3B as L = (2 / 3) * B instead of (3 / 2) * B.
• Mixing up the number of units (for example, confusing 3 balls and 3 pairs of pads).
• Not simplifying fractions cleanly when solving for B in terms of T.

Final Answer:
The cost of one cricket ball is Rs. 16.