Algebra, arithmetic, reasoning.
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When multiplying powers with the same base, add the exponents.
Thus, a³ × a⁵ = a⁸.
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Compound growth gives 20,000 × 1.05².
The result is 22,050.
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The remaining part is 3/4 of the tank.
At 8 hours per full tank, 3/4 takes 6 hours.
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For equal time intervals, average speed is the arithmetic mean.
Thus, (40 + 60)/2 = 50 km/h.
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The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.
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When dividing powers with the same base, subtract the exponents.
Thus, x⁷ ÷ x³ = x⁴.
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Daily work equals total work divided by the number of days.
Thus, A's one-day work is 1/12.
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Daily wage equals total earnings divided by days worked.
Thus, 3,600 ÷ 12 = Rs. 300.
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For opposite directions, relative speeds are added.
Thus, 50 + 70 = 120 km/h.
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The speed is 90 × 5/18 = 25 m/s, so total distance is 25 × 24 = 600 m.
Subtracting the train length gives a bridge length of 400 m.
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Square the coefficient and multiply the exponent by 2.
This gives 2²a⁶ = 4a⁶.
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Their combined daily rate is 1/10 + 1/15 = 1/6.
Therefore, they complete the job in 6 days.
