A classroom has equal number of boys and girls. Eight girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially

## Concept & Logic This is a word problem that requires forming linear equations based on changing quantities. The key insight is correctly equating the modified group sizes based on the ratio given. ## Step-by-Step Solution * Let the initial number of boys be $b$ and the initial number of girls be $g$. * We are told the classroom initially has an equal number of boys and girls. Equation 1: $b = g$ * Eight girls leave, so the new number of girls is $(g - 8)$. The number of boys remains $b$. * The problem states that after this, there are twice as many boys as girls remaining. Equation 2: $b = 2(g - 8)$ * Substitute $b$ with $g$ (since $b = g$) in Equation 2: $g = 2(g - 8)$ * Expand the right side: $g = 2g - 16$ * Solve for $g$: $16 = 2g - g$ $g = 16$ * Since $b = g$, the initial number of boys $b$ is also 16. * The total initial number of students is $b + g = 16 + 16 = 32$. ## Exam Strategy & Shortcut Use the options to work backwards. If the initial total is 32 (Option c), there are 16 boys and 16 girls. If 8 girls leave, 8 girls remain. Are there twice as many boys (16) as girls (8)? Yes. This mental verification is much faster than writing out equations. ## Common Pitfall Students often write $2b = (g - 8)$ instead of $b = 2(g - 8)$. To prevent this, read the phrase "leaving twice as many boys as girls" carefully. It means the number of boys is the larger quantity, so you must multiply the smaller quantity (girls) by 2 to balance the equation. ## Final Answer **Therefore, the correct answer is 32.**