Multiple choice

A farmer earns Rs. Q per hour for working in his field. For every hour he works beyond S hours in a day, he is paid 2.5 times his regular hourly rate. On one particular day, he works for M hours and earns Rs. 1,800 more than his usual daily income. If Q is either 80 or 120, what are the possible values of M and S? (i) 14, 8 (ii) 16, 9 (iii) 18, 12 (iv) 20, 16 (v) 14, 5

  1. Only (i) and (iii)

  2. Only (ii) and (iv)

  3. Only (ii) and (v)

  4. Only (i), (iii) and (v)

  5. All of the above
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D Correct answer
AI explanation

The farmer earns Rs. Q per hour, and for every hour worked beyond S hours, he earns 2.5Q per hour. The extra income of Rs. 1,800 equals the extra hours (M - S) multiplied by 2.5Q, giving the equation 2.5Q(M - S) = 1800. This simplifies to Q(M - S) = 720. If Q = 80, then M - S must equal 9, which is satisfied by option (i) 14, 8 and option (iii) 18, 12. If Q = 120, then M - S must equal 6, which is satisfied by option (v) 14, 5. The possible values are given in Only (i), (iii) and (v).

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