Question Details

Read the following table carefully and answer the questions given below.The table shows total number of EV manufactured by five different companies. The table also shows the percentage of petrol vehicles manufactured out of the total vehicles (diesel, EV and Petrol) manufactured and the percentage of diesel vehicles manufactured out of the total petrol vehicles manufactured by these companies.

Companies Total EV manufactured Percentage of petrol vehicles manufactured Percentage of diesel vehicles manufactured
A 64 60% 40%
B 120 40% 25%
C 171 30% 75%
D 300 25% 60%
E 28 50% 80%

The total number of vehicles (diesel, EV, and petrol) manufactured by A is how many more or less than the total number of diesel vehicles manufactured C, D and B together.

Options

A

500

B

220

C

390

D

420

Show Answer

Correct Answer :

Option B

220

220

Solution :

First, let us understand the relationship between the different types of vehicles manufactured by each company. Let:
- T be the total number of vehicles (Diesel + EV + Petrol) manufactured by a company.
- E be the number of electric vehicles (EV) manufactured.
- P be the number of petrol vehicles manufactured.
- D be the number of diesel vehicles manufactured.

According to the given table details:
1. Petrol vehicles manufactured, P = x %  of  T, where x % is the percentage of petrol vehicles out of the total vehicles.
2. Diesel vehicles manufactured, D = y %  of  P, where y % is the percentage of diesel vehicles out of the petrol vehicles.

We know that the total number of vehicles is the sum of diesel, petrol, and electric vehicles:
T = D + P + E
Substituting D = y % · P into the equation:
T = y % · P + P + E = P ( 1 + y % ) + E
Substituting P = x % · T into the equation:
T = x % · T ( 1 + y % ) + E
Rearranging to solve for the total number of vehicles, T:
T · [ 1 - x % ( 1 + y % ) ] = E
T = E 1 - x % ( 1 + y % )

Step 1: Calculate the total number of vehicles manufactured by Company A
For Company A:
- E = 64
- x % = 60% = 0.6
- y % = 40% = 0.4
Using the formula:
TA = 64 1 - 0.6 · (1 + 0.4)
TA = 64 1 - 0.6 · 1.4 = 64 1 - 0.84 = 64 0.16 = 400
Thus, the total number of vehicles manufactured by Company A is 400.

Step 2: Calculate the diesel vehicles manufactured by Company B
For Company B:
- E = 120
- x % = 40% = 0.4
- y % = 25% = 0.25
Calculating total vehicles TB:
TB = 120 1 - 0.4 · (1 + 0.25) = 120 1 - 0.4 · 1.25 = 120 1 - 0.5 = 240
Calculating petrol vehicles PB:
PB = 40%  of  240 = 96
Calculating diesel vehicles DB:
DB = 25%  of  96 = 24

Step 3: Calculate the diesel vehicles manufactured by Company C
For Company C:
- E = 171
- x % = 30% = 0.3
- y % = 75% = 0.75
Calculating total vehicles TC:
TC = 171 1 - 0.3 · (1 + 0.75) = 171 1 - 0.3 · 1.75 = 171 1 - 0.525 = 171 0.475 = 360
Calculating petrol vehicles PC:
PC = 30%  of  360 = 108
Calculating diesel vehicles DC:
DC = 75%  of  108 = 81

Step 4: Calculate the diesel vehicles manufactured by Company D
For Company D:
- E = 300
- x % = 25% = 0.25
- y % = 60% = 0.6
Calculating total vehicles TD:
TD = 300 1 - 0.25 · (1 + 0.6) = 300 1 - 0.25 · 1.6 = 300 1 - 0.4 = 500
Calculating petrol vehicles PD:
PD = 25%  of  500 = 125
Calculating diesel vehicles DD:
DD = 60%  of  125 = 75

Step 5: Compare the required values
Total vehicles manufactured by Company A, TA = 400.
Total diesel vehicles manufactured by C, D and B together:
DC+D+B = DC + DD + DB = 81 + 75 + 24 = 180.
The difference between the two is:
Difference = 400 - 180 = 220.

Therefore, the total number of vehicles manufactured by A is 220 more than the total number of diesel vehicles manufactured by C, D and B together.

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