A farmer's potato yield this year averaged 30 tonnes per hectare.

Question

A farmer's potato yield this year averaged 30 tonnes per hectare. This was 25% greater than last year's average yield per hectare, but only 1/3 of the projected avergae yield for this year. The projected average yield for this year was what perent greater than last year's average yield?

A. 275%
B. 175%
C. 140%
D. 73 1/3%
E. 58 1/3 %

MartyMurray · Accepted Answer

A farmer's potato yield this year averaged 30 tonnes per hectare. This was 25% greater than last year's average yield per hectare, but only 1/3 of the projected avergae yield for this year. The projected average yield for this year was what perent greater than last year's average yield?

The question tells us that the farmer's yield this year was " only 1/3  of the projected average yield for this year. "

So, the projected yield was 3 times this year's actual yield, or 200 percent greater than the actual yield.

We also see that this year's actual yield was greater than last year's yield.

So, the projection must be even more than 200% greater than last year's yield.

A. 275%
B. 175%
C. 140%
D. 73 1/3%
E. 58 1/3 %

Scanning the answer choices, we see that only A. 275% is greater than 200%.

So, without doing much math, we can choose (A) and complete this question in under a minute.

Correct answer:  A

jack5397 · Answer

X - last year’s yield
Y - Projected Average Yield
30 = 1.25*X
30 = 1/3* Y
X= 24 Y =90

(90-24)/24 *100 = 275%

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rito54 · Answer

Hello! Silly question but how do we know that we have to divide by 24 and not 90. Could someone please explain I get confused every time with this kind of exercise not knowing which value I should divide with.

I know the formula New - Old / Old.

but how does it work here?

Help is much appreciated thank you!

I know the formula New - Old / Old.

but how does it work here?

Help is much appreciated thank you!

MartyMurray · Answer

When we want to know by what percentage one value is "greater than" another, we divide by the value that comes after "greater than" in the question.

This approach makes logical sense because the reference value, or "old" value, is the one that the other value is greater than.

In this case, if we were to divide by 90, then 90 would be the reference value, and we would find the percentage of 90 represented by 24, which is not what the question asks for.

Rather, we need to find the percentage by which 90 is greater than 24.

So, when calculating percentage change, always divide by the reference value. The reference value is the "old" value, or the value such that the decrease or increase is from that value.

The reference value is often named by what follows "greater than," "less than," "percent of," or "change from" in the question.

rito54 · Answer

Thank you very much this is much clearer !

Gaurav07 · Answer

Hey, 
Shouldn't last year's yield be 22.5? you subtract 25% of 30 from 30.

rajpatil.june · Answer

30 is 1/3 of projected yield, 
so projected yield is 90.

also, 30 is 25% greater than last years avg yield, lets say x

5x/4 = 30
x= 24

Projected is what % greater than last year's avg yield.
Means 90 is what % greater than 24.

(90-24)/24*100 = 66/24*100 = 275%

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A farmer's potato yield this year averaged 30 tonnes per hectare.

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A farmer's potato yield this year averaged 30 tonnes per hectare.