Question

Mrs. X spends Rs. 535 in purchasing some shirts and ties for her husband. If shirts cost Rs. 43 each and the ties cost Rs. 21 each, then what is the ratio of the shirts to the ties, that are purchased?

• A. 1 : 2
• B. 2 : 1
• C. 2 : 3
• D. 3 : 4

Hint:

Write the total cost as 43x + 21y = 535 and find the smallest whole-number solution, or test each answer ratio directly against the total.

Answer 1

The Correct Option is B

Since the answer choices are already given as ratios, a quicker approach is to plug each ratio into the cost equation and check whether it gives a whole, sensible number of shirts and ties totalling Rs. 535.

1. Option A (1 : 2): let shirts = k, ties = 2k. Cost = 43k + 21(2k) = 43k + 42k = 85k. Setting 85k = 535 gives k $\approx$ 6.29, not a whole number. Rejected.
2. Option B (2 : 1): let shirts = 2k, ties = k. Cost = 43(2k) + 21k = 86k + 21k = 107k. Setting 107k = 535 gives k = 5, a whole number. This means shirts = 10, ties = 5, and the cost is 43(10) + 21(5) = 430 + 105 = 535, which matches exactly.
3. Option C (2 : 3): let shirts = 2k, ties = 3k. Cost = 86k + 63k = 149k. Setting 149k = 535 gives k $\approx$ 3.59, not whole. Rejected.
4. Option D (3 : 4): let shirts = 3k, ties = 4k. Cost = 129k + 84k = 213k. Setting 213k = 535 gives k $\approx$ 2.51, not whole. Rejected.

Only the 2 : 1 ratio produces a whole number solution that exactly matches the total spend of Rs. 535, confirming option B.