Question

An international NGO for homeless people has supplied certain items for ongoing winters to new shelters for homeless people. These consist of different items like blankets, jackets, shoes, socks, and room heaters. The total number of five items distributed in December 2024 was 3300.
- 24% of all items were blankets.
- $\frac{1}{6}$ of all items were jackets.
- 14% of all items were shoes.
- Remaining items were either socks or room heaters.
- The number of room heaters distributed was 100 more than the number of socks distributed.
What is the difference between the total number of socks and blankets distributed and the number of shoes distributed?

• A. 1022
• B. 1068
• C. 1025
• D. 1028

Hint:

When solving distribution problems involving percentages and unknowns, always calculate known values first, then solve for unknowns using given relationships. Match final result carefully with options provided.

Answer 1

The Correct Option is D

Step 1: Total number of items distributed = 3300 Now calculate each category: Blankets:
\[ 24% \text{ of } 3300 = 0.24 \times 3300 = 792 \] Jackets:
\[ \frac{1}{6} \times 3300 = 550 \] Shoes:
\[ 14% \text{ of } 3300 = 0.14 \times 3300 = 462 \] Socks and Room Heaters:
Total remaining: \[ 3300 - (792 + 550 + 462) = 3300 - 1804 = 1496 \] Let number of socks be $S$.
Then number of room heaters = $S + 100$.
So: \[ S + (S + 100) = 1496 \implies 2S + 100 = 1496 \implies 2S = 1396 \implies S = 698 \] Thus: \[ \text{Socks} = 698, \quad \text{Blankets} = 792, \quad \text{Shoes} = 462 \] Step 2: Calculate required difference.
\[ (\text{Socks} + \text{Blankets}) - \text{Shoes} = (698 + 792) - 462 = 1490 - 462 = 1028 \] \[ \boxed{\text{(D) } 1028} \]