Question

a clock maker has 15 clock faces. each clock requires 1 face and 2 hands. If the clock maker also has 42 hands, how many clocks can be produced? If the clock maker has only 8 hands, how many clocks can be produced?

Answer 1

Ans. Given,

1. 1 clock requires 1 face and 2 hands

2. II. The clock maker has 1 maximum of 15 faces.

Case 1: Number of clock from 42 hands.

            2 hands are required for 1 clock.

            So, maximum number of clocks to be made (theoretically) from 42 hands =

                                    Total number of hands / number of hands required per clock

                                    = 42 hands / 2 hands per clock

                                    = 21 clocks.

However, each clock also requires 1 face, whereas the clock maker has only 15 faces. So, the number of faces is a limiting factor while number of hands is in excess. So, the number of clocks made is limited to the number of faces available with the clock maker.

Therefore, actual number of clocks from 42 hands (in excess) = number of faces (limiting factor)

                        = 15 clocks

(42- 30 hands used in 15 clocks = 12 hands remain unused.)

Case 2: maximum number of clocks to be made (theoretically) from 8 hands =

                                    Total number of hands / number of hands required per clock

                                    = 8 hands / 2 hands per clock

                                    = 4 clocks.

Here, hands are the limiting factor and faces are in excess.