In a forest, the ratio of pine trees to maple trees is 3:4, and the ra

We are given that the ratio of pine trees to maples trees is 3:4; thus:

pine : maple = 3x : 4x

We are also given that the ratio of sycamore trees to maples trees is 4:5; thus:

sycamore : maple = 4y : 5y

Since we see that maple = 4x in the first ratio and maple = 5y in the second ratio, we can multiply the first ratio by 5 and the second by 4 to create a three-part ratio.

pine : maple = 5(3x : 4x) = 15x : 20x

sycamore : maple = 4(4y : 5y) = 16y : 20y

Since the number of maple trees is the same in either ratio, we have 20x = 20y or x = y. Therefore, we can rewrite the ratio of sycamore to maple as:

sycamore : maple = 16x : 20x

Thus, we can write:

pine : maple : sycamore = 15x : 20x : 16x

Finally, since there are 10 more sycamore trees than there are pine trees, we can create the following equation to determine x:

16x = 10 + 15x

x = 10

Since x = 10, there are 15 x 10 = 150 pine trees.

Answer: A

p : m = 3x : 4x

s : m = 4x : 5x ( or, m : s = 5x : 4x )

p : m : s = 15x : 20x : 16x

Now, 16x - 15x = 10

So, x = 10

Hence, total number of pine trees is 15*10 = 150 Pine trees...

Thus, answer will be (A) 150 !!

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Learn to combine the ratios for this questions

Answer: option A

P/M = 3/4--------------(a)
S/M =4/5 or M/S = 5/4-----(b)

multiply (a) & (b) to get
P/S= 15/16
or S = 16P/15-------(c)

Also given P+10=S

substituting S from (c) we get
P+10= 16P/15
or P=150

Ans A

P : M = 3x : 4x => 15x : 20x
S : M = 4x : 5x +> 16x : 20x

So, P : M : S = 15x : 20x : 16x

Now, 16x - 15x = 10

Or, x = 10

So, No of Pine trees is 15*10 = 150

Thus, answer will be (A) 150

We are given that the ratio of pine trees to maple trees is 3:4 and that the ratio of sycamore trees to maple trees is 4:5. Thus:

pine trees : maple trees = 3 : 4

and

sycamore trees : maple trees = 4 : 5

Since we have maples trees in both ratios (4 and 5), let’s use the LCM of 4 and 5, which is 20, to equate the two ratios.

We can multiply the entire first ratio by 5 and the entire second ratio by 4, and we have:

pine trees : maple trees = 15 : 20

and

sycamore trees : maple trees = 16 : 20

Thus, our three-part ratio becomes:

pine trees : maple trees : sycamore tree = 15 : 20 : 16

or

pine trees : maples trees : sycamore tree = 15n : 20n : 16n (in which n is a multiplier)

Since there are ten more sycamore trees than pine trees, we have:

16n = 15n + 10

n = 10

Thus, there are 15 x 10 = 150 pine trees.

Answer: A