Mathematics
Shikha works in a factory. In one week she earned ₹390 for working 47 hours, of which 7 hours were overtime. The next week she earned ₹416 for working 50 hours, of which 8 hours were overtime. What is Shikha's hourly earning rate ?
Linear Equations
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Answer
Let's assume earning's of Shikha be ₹x per hour for regular hour and ₹y per hour for overtime.
Then according to the conditions given in the problem,
40x + 7y = 390 ……(i)
and,
42x + 8y = 416 …….(ii)
Multiplying (i) by 8 and (ii) by 7 we get,
320x + 56y = 3120 …….(iii)
294x + 56y = 2912 …….(iv)
Subtracting (iv) from (iii) we get,
⇒ 320x + 56y - (294x + 56y) = 3120 - 2912
⇒ 26x = 208
⇒ x = 8.
Substituting value of x in (i) we get,
⇒ 40(8) + 7y = 390
⇒ 320 + 7y = 390
⇒ 7y = 70
⇒ y = 10.
Hence, Shikha's earning is ₹8 per regular hour and ₹10 per hour for over time.
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