The bar graph shows the total item manufactured by four companies A, B, C and…

Concept

In a manufactured-vs-sold bar chart, the quantity actually moved is read directly off the relevant bar, and the quantity left over (unsold) is the manufactured amount minus the sold amount for the same company. A ratio between two such groups is formed by summing the required quantities for each group and then reducing the fraction by their greatest common divisor.

Reading the values from the graph

1. A: manufactured = 120, sold = 80

2. B: manufactured = 96, sold = 76

3. C: manufactured = 140, sold = 120

4. D: manufactured = 80, sold = 60

Application

1. Items sold by A and B together = 80 + 76 = 156.

2. Unsold items of C = manufactured - sold = 140 - 120 = 20.

3. Unsold items of D = manufactured - sold = 80 - 60 = 20.

4. Unsold items of C and D together = 20 + 20 = 40.

5. Required ratio = 156 : 40. Divide both terms by their GCD, 4: 156 / 4 = 39 and 40 / 4 = 10, giving 39 : 10.

Cross-check

Reverse the reduction: 39 x 4 = 156 and 10 x 4 = 40, which reproduces 156 : 40, the un-reduced ratio. The profit figures printed in the note below the graph are not needed here, since the question asks only about sold and unsold quantities.

Required ratio = 39 : 10.