Question

A labourer was engaged for 30 days on the condition that he will be paid Rs. 35 for each day he works and will be fined Rs. 10 for each day he is absent. If he earned Rs. 735 in total, then the number of days he worked is …………………. 

A) 21 

B) 22 

C) 25 

D) 23

Answer 1

Correct option is (D) 23

Let labourer works x number of days and absent y days.

\(\because\) Total number of days he engaged = 30

\(\therefore\) x+y = 30             ___________(1)

Labourer earned Rs. 735 in total.

\(\therefore\) 35x - 10y = 735  ___________(2)

Put y = 30 - x from (1) into (2), we get

35x - 10 (30 - x) = 735

\(\Rightarrow\) 35x - 300 + 10x = 735

\(\Rightarrow\) 45x = 735+300 = 1035

\(\Rightarrow\) x = \(\frac{1035}{45}\) = 23

\(\therefore\) y = 30 - x = 30 - 23 = 7    (From (1))

Hence, number of days he worked is x = 23.

Answer 2

Correct option is D) 23