Johnston Booksellers currently generates $50,000 in annual sales reven

Question

Johnston Booksellers currently generates $50,000 in annual sales revenue. Its competitor, Trevor Books, currently generates $490,000 in annual sales revenue. The sales revenue generated by Johnston Booksellers is increasing each year at a constant rate, while the sales revenue generated by Trevor Books is decreasing each year at a constant rate. If Johnston continues to generate an increased amount of revenue annually at its constant rate and Trevor continues to generate a decreased amount of revenue annually at its constant rate, in four years the bookstores will earn the same amount of annual sales revenue. After the four-year mark, Johnston Booksellers will receive more sales revenue per year than Trevor Books.

In the table below, identify the rates of increase or decrease, in annual revenue earned, for each bookstore that together meet the revenue forecasts described above. Select only one option in each column.

Apt0810 · Answer

50000+4J= 490000-4T
440000=4T+4J
So T+J= 110000
So per the above equation and the answer options J= 90000 and T = 20000
Where J is rate of increment for Johnston bookseller
While T is rate of decrement for Trevor bookseller

Posted from my mobile device

lwx939431 · Answer

Based on the above argument, J=50000 and T=60000 also give the same answer

kntombat · Answer

Sajjad1994 , I solved the question and I got 2 sets of answers.
1.) Johnston Booksellers => 20,000 and Trevor Books => 90,000.
2.) Johnston Booksellers => 50,000 and Trevor Books => 60,000.

which is the correct OA ?

Sajjad1994 · Answer

The correct answer is $90,000 per year for Johnston Booksellers and $20,000 per year for Trevor Books.

Thank you

Baps · Answer

Hi  Sajjad1994 ,

Why do we have to pick $90,000 and $20,000 over $60,000 and $50,000? What does the official explanation say about that? Thanks!

rocky620 · Answer

Baps

50000 & 60000, Revenues after 4 years of:   
 Case-1 
Johnson = 50000 + (50000*4) = 240000
Trevor = 490000 - (60000*4) = 250000

Case-2 
Johnson = 50000 + (60000*4) = 290000
Trevor = 490000 - (50000*4) = 290000

Both these cases does no satisfy our condition. The same can be done for 20000 & 90000 respectively.

Sajjad1994 · Answer

Official Explanation

If Johnston Booksellers increases its sales revenue by $90,000 per year, in 4 years it will earn $410,000 in annual revenue. If Trevor Books decreases its sales revenue by $20,000 per year, in 4 years it will also earn $410,000 in annual revenue. After the 4th year, Johnston Booksellers will generate more sales revenue each year than Trevor Books.

Sahadeva · Answer

The annual sales after 4th year i.e. in the 5th year should be greater than 490k. For this scenario, we have to pick $90,000 and $20,000 over $60,000 and $50,000. 
Johnson = 50k + 5x90k = 500k (> 490k)

Oppenheimer1945 · Answer

This is a highly poor quality ques Sajjad, violating the mathematical language.  The rate of increase is % in mathematical terms. You're wrongly taking it as AP series.
 Bunuel  you can comment.

This should be 50000(1+a/100)^4=490,000(1-b/100)^4 and not 50000+4a=490000-4b.

Bunuel · Answer

Agree. The wording is ambiguous. Archiving the question.

Johnston Booksellers currently generates $50,000 in annual sales reven

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Johnston Booksellers	Trevor Books	Rate of increase or decrease (dollars per year)
		10,000
		20,000
		50,000
		60,000
		90,000
		180,000