(i) Option (c): New volume (l + 1)wh minus original lwh gives wh cubic units. (ii) Option (e): π(r + 1)²h − πr²h = 2πrh + πh cubic units. (iii) Volume decreases by (4/3)π(3r² − 3r + 1) cubic units. Ganita Manjari Part ...
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Let the father’s age be F, which equals children’s sum S. In 20 years, children gain 4 × 20 = 80 years: F + 80 = 2(F + 20). This gives F + 80 = 2F + 40, so F ...
Let speed be s and time t. The conditions give (s + 6)(t − 6) = st and (s − 4)(t + 6) = st, simplifying to t − s = 6 and 3s − 2t = 12. Solving yields ...
Opposite angles sum to 180°, giving x + 3y = 150 and 4x + y = 160. Solving gives x = 30 and y = 40. The angles are ∠A = 37°, ∠B = 48°, ∠C = 143° and ∠D ...
Let the number be 10x + y. Then x + y = 15 and (10y + x) − (10x + y) = 9, which simplifies to y − x = 1. Adding both equations gives 2y = 16, so y ...