Problem Solving

Hello,

For the following:

Company XYZ sells buses and cars only. Last year 75% of the revenue came from car
sales, the rest from bus sales. If this year car sales grew by 10% and bus sales grew by
30%, what was the total percent increase in sales?

(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

I am getting E but the OA says C. Can you please tell me which is correct?

My approach:

Let total revenue last year be $100.
Rev. from Bus sales = $75
Rev. from car sales = $25

Rev. from Bus sales this year = $390/4
Rev. from car sales this year = $110/4
Hence, total rev. this year = $500/4

Hence, 25% increase.


Thanks for your help,
Sri

gmattesttaker2 wrote:Hello,

For the following:

Company XYZ sells buses and cars only. Last year 75% of the revenue came from car
sales, the rest from bus sales. If this year car sales grew by 10% and bus sales grew by
30%, what was the total percent increase in sales?

(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

I am getting E but the OA says C. Can you please tell me which is correct?

Approach 1:
Last year, 75% of revenue came from car sales.
Implication:
Of every $4 dollars earned, $3 were from car sales, while $1 was from bus sales.

This year, car sales increased by 10%, while bus sales increased by 30%.
Thus, of every $4 earned last year, $3 increased by 10%, while $1 increased by 30%.
Average percent increase for every $4 in revenue = (3*10 + 1*30)/4 = 60/4 = 15%.

The correct answer is C.

Approach 2:
75% = 3/4.
10% = 1/10.
Let last year's total revenue = the product of the denominators = 4*10 = $40.

Last year, car sales accounted for 3/4 of total revenue.
Thus, car sale revenue = (3/4)(40) = $30, while bus sale revenue = 40-30 = $10.

This year, car sales increased by 10%, while bus sales increased by 30%.
Thus, the increase in car sale revenue = 10% of 30 = $3, while the increase in bus sale revenue = 30% of 10 = $3.
Total increase in revenue = 3+3 = $6.
Percent increase in revenue = (increase)/(last year's revenue) = 6/40 = 3/20 = 15/100 = 15%.

The correct answer is C.

gmattesttaker2 wrote:Last year 75% of the revenue came from car
sales, the rest from bus sales.

My approach:

Let total revenue last year be $100.
Rev. from Bus sales = $75
Rev. from car sales = $25

Sri, the question says that last year 75% of the revenue came from car sales, but you plugged in only $25 for car sales. This may be the source of your error.

-Patrick
GMATFix

Sri, you had the right idea - I think you just got the sales figures backwards. (Car sales should be $75, bus sales should be $25.) Don't fret, though, it happens: if I had a quarter for every time I've done something like this myself, I'd be able to buy a bus and car dealership myself! The important thing is that your idea was right.

Total initial revenue is of last year =100$
Total initial revenue from car sales =75$
Total initial revenue from bus sales =25$

Total increase in car sales is 10%=>10% of 75=7.5
Total increase in bus sales =30%=>30% of 25=>25*3/10=7.5

total revenue this year due to car sales is 82.5$=>75+7.5
total revenue this year due to bus sales is 32.5=>25+7.5
total revenue generated this year from sales is 115.0

total revenue from last years sales is 100$

therefore percentage increase is (115-100)/100

15% answer (C)

Patrick_GMATFix wrote:

gmattesttaker2 wrote:Last year 75% of the revenue came from car
sales, the rest from bus sales.

My approach:

Let total revenue last year be $100.
Rev. from Bus sales = $75
Rev. from car sales = $25

Sri, the question says that last year 75% of the revenue came from car sales, but you plugged in only $25 for car sales. This may be the source of your error.

-Patrick
GMATFix

Hello Patrick,

Thanks for the tip. I had the wrong amounts in my solution.

Best Regards,
Sri

Matt@VeritasPrep wrote:Sri, you had the right idea - I think you just got the sales figures backwards. (Car sales should be $75, bus sales should be $25.) Don't fret, though, it happens: if I had a quarter for every time I've done something like this myself, I'd be able to buy a bus and car dealership myself! The important thing is that your idea was right.

Hello Matt,

Thanks for the tip and for your help.

Best Regards,
Sri

Matt@VeritasPrep wrote:Sri, you had the right idea - I think you just got the sales figures backwards. (Car sales should be $75, bus sales should be $25.) Don't fret, though, it happens: if I had a quarter for every time I've done something like this myself, I'd be able to buy a bus and car dealership myself! The important thing is that your idea was right.

Hello Matt,

Thanks for the tip and for your help.

Best Regards,
Sri

A simple solution that you can have to this question is by assuming values.
For Example: Let the total revenues be 100$
So Revenue from Car Sales initially will be 75% of 100$ i.e. 75$
And Revenue from Bus Sales would be 100$-75$ = 25$ which is the remaining amount from the total revenues.
Now the question states that the revenues from car sales increase by 10% i.e. 10% of 75$ which is 7.5$
And the revenues from bus sales increase by 30% which is also 7.5$ (30% of 25$)
Now that we have an individual increase in the revenues from Car sales and Bus sales,
all we have to do now is add the initial total revenue with the individual increases in the revenues from car and bus sales i.e. 100$+7.5$+7.5$ = 115$
Hence, resulting into an increase of 15$ compared to the initial total revenues. Thereby giving us an increase of 15% which is the answer.