Ogel Limited sells toys and books only. It’s revenues from toys sales

Question

Ogel Limited sells toys and books only. It’s revenues from toys sales in 2015 were up 12% from 2014 and revenues from books sales in 2015 were down by 17% from 2014. If the total revenues from toys sales and books sales in 2015 were down by 2% from 2014, what is the ratio of revenue from toys sales in 2014 to revenue from books sales in 2014?

A. 2: 17
B. 12: 17
C. 9: 11
D. 13: 14
E. 15: 14

A. 2: 17
B. 12: 17
C. 9: 11
D. 13: 14
E. 15: 14

IanStewart · Accepted Answer

It's just a weighted average problem: toys have an 'average' of +12%, books have an 'average' of -17%, and combined the two groups have an 'average' of -2%. Since -2 is (slightly) closer to 12 than to -17, toy revenues were (slightly) greater than book revenues, and the only answer choice that is bigger than 1 to 1 is E, so it has to be right.

If we needed to find the exact value of the ratio, using "alligation" we just need to do two subtractions: -2-(-17) = 15 and 12-(-2) = 14, so the groups are in a 15 to 14 ratio. I won't explain that method here, but there are lots of places that explain it in detail.

gadde22 · Answer

Let's say in 2014 toys revenue = x and books revenue = y

In 2015 toys revenue = 1.12x
And books revenue. = 0.83y

Total revenue in 2014 = x + y

Total revenue in 2015 = 0.98(x + y)

So from the question, 
1.12x + 0.83y = 0.98(x + y)

0.14x = 0.15y
 X/Y= 15/14

So E is the correct answer.

Posted from my mobile device

ScottTargetTestPrep · Answer

Solution:

We can use the following fact:

If the overall percent change the two groups, group A and group B, combined is m, group A has a percent change of a (where a < m) and group B has a percent change of b (where b > m), then the ratio of group B to group A is (m - a)/(b - m).

Using the fact above (by letting the revenue of toys to be group B and the revenue of books to be group A), we have (notice that here, m = -2, b = 12, a = -17):

revenue of toys/revenue of toys = (-2 - (-17))/(12 - (-2)) = 15/14.

Answer: E

luisdicampo · Answer

Deconstructing the Question

Let revenue from toys in 2014 be   T   and from books be   B  .

In 2015, toys increase by   12\%   and books decrease by   17\%  .

Total revenue in 2015 is   2\%   less than in 2014.

Step-by-step

So

1.12T + 0.83B = 0.98(T + B)

Expand:

1.12T + 0.83B = 0.98T + 0.98B

Rearrange:

1.12T - 0.98T = 0.98B - 0.83B

0.14T = 0.15B

Thus

\frac{T}{B} = \frac{0.15}{0.14} = \frac{15}{14}

Answer: E

Ogel Limited sells toys and books only. It’s revenues from toys sales

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Ogel Limited sells toys and books only. It’s revenues from toys sales

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