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

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

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.

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

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.

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 ?

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.

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

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