The table shows the percentage (%) distribution of production of bicycles of two different models (L and M) by the six companies A-F, ratio of production of model L. to that of M, and the percent (%) profit earned on these two models. Production cost of the six companies together is Rs 64 Crore.
Company Wise Bicycle Production and Profit
| Company |
% Distribution of Production of Bicycles |
Production Ratio |
% Profit |
||
| L | M | L | M | ||
| A | 20% | 13 | 7 | 25% | 32% |
| B | 14% | 9 | 5 | 28% | 30% |
| C | 22% | 6 | 5 | 20% | 24% |
| D | 13% | 6 | 7 | 35% | 25% |
| E | 10% | 2 | 3 | 24% | 21% |
| F | 21% | 11 | 10 | 30% | 20% |
The ratio of the profit earned on model L. by Company B to that of model M by Company D is
Correct Answer :
36:25
Solution :
The correct option is 36:25.
Let us find the step-by-step ratio of the profit earned on model L by Company B to that on model M by Company D.
Let the total cost of production of all six companies together be denoted by C. We are given that C = Rs 64 Crore.
Step 1: Calculate the profit earned on model L by Company B
From the table, the parameters for Company B are:
- Percentage distribution of production: 14% of the total production cost.
- Production ratio of L to M: 9 : 5.
- Percent profit on model L: 28%.
Thus, the cost of production for Company B is:
Since the ratio of production cost of model L to model M for Company B is 9 : 5, the cost of production of model L by Company B is:
The profit earned on model L by Company B is 28% of its production cost:
Step 2: Calculate the profit earned on model M by Company D
From the table, the parameters for Company D are:
- Percentage distribution of production: 13% of the total production cost.
- Production ratio of L to M: 6 : 7.
- Percent profit on model M: 25%.
Thus, the cost of production for Company D is:
Since the ratio of production cost of model L to model M for Company D is 6 : 7, the cost of production of model M by Company D is:
The profit earned on model M by Company D is 25% of its production cost:
Step 3: Find the ratio of the two profits
Now we divide the profit of model L by Company B by the profit of model M by Company D:
Canceling the common percentage units and total cost C:
Since , we simplify the expression:
Thus, the required ratio is 36:25.
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