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Example 5: The sum of two numbers is 15 and sum of their reciprocals is . Find the
numbers.

Ans: Let the two numbers be x and 15 - x, so that their sum is 15.

According to the given condition, sum of the reciprocal of the numbers is , i.e

50 = 15x - x 2
2
x - 15x + 50 = 0
2
x - 10x - 5x + 50 = 0
x(x - 10) - 5(x - 10) = 0

(x - 10)(x - 5) = 0
Either x - 10 = 0 or x - 5 = 0
Either x = 10 or x = 5
(i) When x = 10, then 15 - x = 15 - 10 = 5

(ii) When x = 5, then 15 - x = 15 - 5 = 10
Hence, the two numbers are 5 and 10.

Example 6: A motor boat whose speed in still water is 15 km /hr goes 30 km

downstream and returns back to the starting point in a total time of hours.
Find the speed of the stream.

Ans: Let the speed of the stream be x km /hr.
Then, the downstream speed = (15 + x) km/hr
And, the upstream speed = (15 - x) km/hr

Time taken to cover 30 km downstream =

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