Question Detail

Beam weight acts at centre (5 m from ends). Pivot at centre. Let left end be 20 kg girl at 0 m, right end be 40 kg girl at 10 m. Moments about pivot: Left side moment = 20g × 5 (since distance from pivot to left end is 5 m) = 100g. Right side moment = 40g × 5 = 200g. Net clockwise = 100g (if left side considered anticlockwise). To balance, add 25 kg mass on left side at distance d from left end (so from pivot = d - 5). Moment from 25 kg = 25g × (d - 5) anticlockwise. For equilibrium: 100g + 25g(d-5) = 200g → 100 + 25(d-5) = 200 → 25(d-5) = 100 → d-5 = 4 → d = 9 m from left end. Distance from 20 kg girl = 9 m, not in options. If mass placed on right side: 200g + 25g(5 - d) = 100g → 25(5-d) = -100 → 5-d = -4 → d=9 m same. If pivot at middle, the 25 kg must be at 9 m from left, which is 4 m from the right end? Options are 4 m, 1 m, 6 m, 3 m. 4 m from left would be at 4 m, then distance from pivot = 1 m left, moment = 25g, then total left = 100g+25g=125g, right=200g, not balanced. So maybe they want distance from 20 kg girl to the 25 kg mass, which could be 4 m if the 25 kg is at 4 m from left? That gives 25g at 4 m (1 m left of pivot) moment 25g, left total 125g, right 200g, not balanced. So likely the correct answer is 4 m if the 25 kg is placed at 6 m from left? At 6 m from left is 1 m right of pivot, moment = 25g clockwise, then right total = 200g+25g=225g, left=100g, not balanced. So none balance. Possibly the beam weight is not considered.