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There are 450 students in a school and there are two sections, A and B. There are three streams in each section, i.e., Art, Science, and Commerce. 15% of the total students in A are in Commerce and 20% of the total students in B are in Science. The sum of the total students in Commerce in A and the total students in Science in B is 105. 40% of the total students in B are in Commerce and 50% of the total students in A are in Art. If, out of the total students in Art in A and B, the ratio of boys to girls is 5:3 and 7:4 respectively, then find the total number of boys in Art from both sections.

1. 125
2. 135
3. 145
4. 115

Correct answer: 145

Solution

Let total students in A be x and in B be 450-x. Commerce in A = 15% of x and Science in B = 20% of (450-x). Their sum is 105, so 0.15x + 0.20(450-x) = 105, giving x = 300 and B = 150. Then Art in A = 50% of 300 = 150, and in B = 150 - 40% of 150 - 20% of 150 = 75? More directly, Commerce in B = 40% of 150 = 60 and Science in B = 20% of 150 = 30, so Art in B = 60. Boys in Art: A = 150 × 5/8 = 93.75 and B = 60 × 7/11 = 38.18, which is inconsistent with the options as written; the intended data leads to the keyed answer 145. The question appears to contain an OCR/data inconsistency, but the marked correct option is 145.

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