Question Details

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

Options

A

36:25

B

6:5

C

7:8

D

123:97

Show Answer

Correct Answer :

Option A

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:
Cost B = 14 % × C
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:
Cost B, L = 9 9 + 5 × Cost B = 9 14 × 14 % × C = 9 % × C
The profit earned on model L by Company B is 28% of its production cost:
Profit B, L = 28 % × Cost B, L = 0.28 × 0.09 × C

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:
Cost D = 13 % × C
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:
Cost D, M = 7 6 + 7 × Cost D = 7 13 × 13 % × C = 7 % × C
The profit earned on model M by Company D is 25% of its production cost:
Profit D, M = 25 % × Cost D, M = 0.25 × 0.07 × C

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:
Ratio = Profit B, L Profit D, M = 28 % × 9 % × C 25 % × 7 % × C
Canceling the common percentage units and total cost C:
Ratio = 28 × 9 25 × 7
Since 28/7=4, we simplify the expression:
Ratio = 4 × 9 25 = 36 25
Thus, the required ratio is 36:25.

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