Algebra, arithmetic, reasoning.
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An event and its complement have total probability 1.
Thus, P(not A) = 1 - 0.35 = 0.65.
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The pipe fills 1/6 of the tank per hour.
In 2 hours it fills 2/6 = 1/3.
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Distance equals speed multiplied by time.
Thus, 72 × 2.5 = 180 km.
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Time is inversely proportional to speed.
The decrease is 1 - 50/60 = 1/6 = 16 2/3%.
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The required numbers multiply to 6 and add to 5.
Those numbers are 2 and 3.
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Sales tax is 12% of Rs. 5,000, or Rs. 600.
The total payable amount is Rs. 5,600.
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Their combined rate is 1/8 + 1/12 = 5/24 tank per hour.
Time is 24/5 = 4.8 hours.
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To convert km/h to m/s, multiply by 5/18.
Thus, 54 × 5/18 = 15 m/s.
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Let total distance be 3d; time is d/30 + 2d/60 = d/15.
Average speed is 3d ÷ (d/15) = 45 km/h.
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The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
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Commission is 6% of total sales.
Thus, 0.06 × 250,000 = Rs. 15,000.
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The net rate is 1/10 - 1/15 = 1/30 tank per hour.
Therefore, the tank fills in 30 hours.
