Based on this year's costs, an orcharde grower budgets P

Question

Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 25% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be

A) 20% less than N
B) 25% less than N
C) equal to N
D) 20% greater than N
E) 25% greater than N

A) 20% less than N
B) 25% less than N
C) equal to N
D) 20% greater than N
E) 25% greater than N

rohityes · Accepted Answer

Current Year 
N = Number of Trees
C = Cost of Planting 1 Tree
P = Total Budget

P = N * C  .......( i )

Next Year 
M = Number of Trees
1.25C = Cost of Planting 1 Tree
P = Total Budget

P = M * 1.25C
NC = M * 1.25 C  .......using (i) 
M = (1/1.25)N
 M = 0.8N

Hence 20% less than N

Ans A.

Bunuel · Answer

General formula for percent increase or decrease, (percent change):  percent=\frac{Change}{Original}*100 .

Though this problem is fairly straightforward: if $1 buys 1 tree for 1$, then the same $1 will by $1/1.25=0.8 trees, which is 20% less.

Answer: A.

Oski · Answer

Correct answer is (A).

This year, the price of a tree is price1=P/N.

If this price increases by 25% it becomes price2=P/N*1.25

Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.25) i.e. N/1.25 i.e. .80*N

GMATBLACKBELT · Answer

Just plug in #'s.

160/16= 10 Trees. 160/20= 8 Trees.

The new trees are .8 of N.

Thus A.

Or you could just see that P/1.25N --> New Price = .8P/N New Tree --> P/.8P/N --> .8N

alpha_plus_gamma · Answer

A.

this year, the cost to plant one tree is P/N dollars, it will become 5/4*P/N next year. In P dollars one can plant P/(5P/4N)
i.e. 4/5* N trees which is 80%of N thus 20%less than N

MHIKER · Answer

Let P = 100, N = 25, cost per tree 100/25 = 4
25% increase of cost = 4*125% = 5
Total tree can be purchased with the same ($100) amount = 100/5 = 20, which is 5 less than previous
5/25*100 = 20% Less than N
Ans. A

priyalr · Answer

Hi, I got confused with the absence of numbers. So here's how I did it.

Lets say it costs 16$ - 1 mango
 160$ - 10 mangoes
According to qustn, the price of each mango increased by 25%, so now price of ach mango = 16+ 16*25/100= 20
So now 1 mango costs= $20.

Now in 160$ he can buy 160/20= 8 mangoes, ie. 20% less than at previous rate.

Basically what I did is I used the figuers of qustn, in a simple problem to get my ans. It took me less than 2 min to get correct ans. Pls let me know if I've used the right method ?

Bunuel · Answer

Yes, your method is correct. If you read the solutions above, you'll see that most of them use basically the same approach just with different numbers.

JeffTargetTestPrep · Answer

If it’s on budget, then the cost per tree is P/N. Since the average cost were to increased by 25%, the cost per tree will the be 1.25(P/N) = 1.25P/N. Therefore, the number of trees that can be planted is:

P/(1.25P/N) = PN/(1.25P) = N/1.25 = 4N/5 = (80/100)N

We see that only 80% of the trees can be planted with P dollars, which is a 20% decrease from the original number of trees.

Alternate Solution:

Let’s assume that the grower budgets $100 this year for planting N = 100 trees. Thus, it will cost $1 per tree for planting. Next year, a 25% increase raises the cost per tree to $1.25. With the budget still at $100, it means that the grower can plant only 100/1.25 = 80 trees, which is 20% less than what he can plant this year.

Answer: A

bumpbot · Answer

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Based on this year's costs, an orcharde grower budgets P

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