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Word problem - percentages

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by Uva@90 » Mon May 11, 2015 6:44 pm
Hi All,

Company A has four different departments - Printing, Grooming, Offsetting and Distribution which together form the entire company A. The revenue earned from Printing was 60% of the company's total revenue in the month of January. In February however, the Printing department earned 20% more than in January. The revenue for the remaining department was same for both months. Approximately what percent of the company's revenue did the printing division earn for the month of February ?

A) 64%
B) 68%
C) 72%
D) 76%
E) 80%

OA C

However I got OA as A

below is how I did, can anyone explain what mistake I did,

For Jan,
TJ = PJ + GJ + OJ + DJ --- 1

TJ-PJ = GJ+OJ+DJ ---2

Since printing is 60 % of total revenue
PJ = 3/5 * TJ ------ 3

For Feb,
TB = PB + GJ + OJ + DJ ---4 (Since Grooming, Offsetting and Distributions remains same.)

PB = 120% PJ ==> PB = (120/100)*(3/5)*TJ ==> (18/25)TJ ----5

Substitute 2,3 and 5 in 4

TB = (18/25)TJ + TJ -(3/5)TJ

TB = (28/25)TJ ==> TJ = (25/28)TB --6

Substitute 6 in 5

PB = (18/25)*(25/28)TB ==> PB = (9/14) TB
Hence 64 %

But is wrong as per OA.

Can any one tell me what wrong I did ?

Thanks in advance.
Regards,
Uva.
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by talaangoshtari » Mon May 11, 2015 9:14 pm
TJ=PJ+GJ+OJ+DJ
TF=PF+GJ+OJ+DJ
TJ-PJ=TF-PF
(TJ-PJ)/(TF-PF)=1
On the other hand we have
PJ=60/100TJ,
substitute it in the equation,so we have:
TJ=(25/28)TF, and PJ=60/100TJ,therefore TJ=50/36PF,so we have:
PF=64%TF
so the answer is 64%
Last edited by talaangoshtari on Mon May 11, 2015 10:25 pm, edited 2 times in total.
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by [email protected] » Mon May 11, 2015 9:30 pm
Hi Uva@90,

Your answer is correct. What is the source of this question? It's possible that the OA is a typo.

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by Uva@90 » Mon May 11, 2015 11:49 pm
[email protected] wrote:Hi Uva@90,

Your answer is correct. What is the source of this question? It's possible that the OA is a typo.

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Thanks Rich,

This Question is from "Crack Verbal".

Regards,
Uva.
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by theCEO » Tue May 12, 2015 1:36 am
Uva@90 wrote:Hi All,

Company A has four different departments - Printing, Grooming, Offsetting and Distribution which together form the entire company A. The revenue earned from Printing was 60% of the company's total revenue in the month of January. In February however, the Printing department earned 20% more than in January. The revenue for the remaining department was same for both months. Approximately what percent of the company's revenue did the printing division earn for the month of February ?

A) 64%
B) 68%
C) 72%
D) 76%
E) 80%

OA C

However I got OA as A

below is how I did, can anyone explain what mistake I did,

For Jan,
TJ = PJ + GJ + OJ + DJ --- 1

TJ-PJ = GJ+OJ+DJ ---2

Since printing is 60 % of total revenue
PJ = 3/5 * TJ ------ 3

For Feb,
TB = PB + GJ + OJ + DJ ---4 (Since Grooming, Offsetting and Distributions remains same.)

PB = 120% PJ ==> PB = (120/100)*(3/5)*TJ ==> (18/25)TJ ----5

Substitute 2,3 and 5 in 4

TB = (18/25)TJ + TJ -(3/5)TJ

TB = (28/25)TJ ==> TJ = (25/28)TB --6

Substitute 6 in 5

PB = (18/25)*(25/28)TB ==> PB = (9/14) TB
Hence 64 %

But is wrong as per OA.

Can any one tell me what wrong I did ?

Thanks in advance.
Regards,
Uva.
Alternative approach:
assume that the revenue earned from Printing was $60 and total revenue was $100 for January

Jan total revenue = revenue from printing + other departments
100 = 60 + 40

Feb. printing revenue = 1.2 * 60 = $72
Feb total revenue = 72 + 40 = 112

72/112 = 9/14 = 7/14 + 2/14 = 0.5 + 1/7 = 0.5 + 0.14 = 0.64 =>64%
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by [email protected] » Tue May 12, 2015 9:10 am
Hi Uva@90,

Did the question come with an explanation? It would be interesting to see if the original author truly made a mistake or if the OA was just mis-marked.

Answer C is the answer you would come up with IF you raised the revenue from the Printing Department but did NOT raise the Overall Revenue for February; it's essentially an organizational/math error.

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