Question

An orchard is an area of land where fruit trees are grown. In an orchard
orange trees or other citrus trees are not grown. Ram had an orchard with certain number of
apple trees. He had to cut down five trees to control the insects. Each of the remaining trees
produced 210 apples, producing a total harvest of 41,790 apples.
Answer the following questions:
(a) How many trees did Ram’s orchard have initially?
(b) What is the total harvest produced if no tree is cut?
(c) If number of trees cut down decrease by 2 and each tree
produced 6 apples more, then what is total harvest?
(d)If trees were 300 and total harvest 62,500, each tree producing 250 apples, then how
many trees were cut?
(e) Ram’s harvest depends on
(i) number of trees cut. (ii) apples produced by each tree.

Answer 1

Question :

An orchard is an area of land where fruit trees are grown. In an orchard orange trees or other citrus trees are not grown. Ram had an orchard with certain number of apple trees. He had to cut down five trees to control the insects. Each of the remaining trees

produced 210 apples, producing a total harvest of 41,790 apples. Answer the following questions:

(a) How many trees did Ram’s orchard have initially?

(b) What is the total harvest produced if no tree is cut?

(c) If number of trees cut down decrease by 2 and each tree produced 6 apples more, then what is total harvest?

(d) If trees were 300 and total harvest 62,500, each tree producing 250 apples, then how many trees were cut?

(e) Ram’s harvest depends on

(i) number of trees cut.

(ii) apples produced by each tree.

(iii) both (i) and (ii)

(iv) None

Solution :

a) Total no of apples grown → 41,790

Each tree can produce 210 apples

$\sf \therefore No \: of \: trees \rarr \frac{total \: no \: of \: apples}{apple \: produced \: by \: one \: tree}$

$\sf \small \rarr \frac{41790}{210}$

199

• So there are 199 trees in the orchard

_____________________________________________

b) So according to the question 5 trees are cut and the no of trees we got is 199

If we don't cut 5 trees so

Total no of trees = 199 + 5 = 204

Now as we know each tree produces 210 apples

So 204 trees will produce → 204 × 210 apples

→ 42840

• So the total harvest will be 42840 apples

_______________________________________________

c) So here acc. to the question

2 trees are decreased from total = 199 – 2 → 197 trees

Each trees produces 6 apples more than usual

so 210 + 6 = 216 apples

So the total harvest becomes → 197 × 216

→ 42552

• So now the harvest has 42552 apples

_______________________________________________

d) Total harvest = 62500 apples

Total no of trees = 300

Apples produced by each tree → 300 × 250

→ 75000

Total harvest with 300 trees = 75000 apples

So difference in apples = 75000 – 62500 → 12500

$\sf \small No \: of \: trees \rarr \frac{difference \: in \: apples}{apples \: produced \: by \: each \: trees}$

$\sf \small \rarr \frac{12500}{250}$

→ 50

• So 50 trees were cut down

_______________________________________________

e) Ram's harvest depends on the number of trees cut and apples produced by each tree

• So the correct answer is option (iii)

Final Answers :

a) there are 199 trees in the orchard

b) the total harvest is 42840 apples

c) the harvest has 42552 apples

d) 50 trees were cut down

e) correct answer is option (iii)

Answer 2

${\huge{\bf{\underline{\underline{\red{Given :}}}}}}$

An orchard is an area of land where fruit trees are grown. In an orchard orange trees or other citrus trees are not grown. Ram had an orchard with certain number of apple trees. He had to cut down five trees to control the insects. Each of the remaining trees produced 210 apples, producing a total harvest of 41,790 apples.

______________________

${\huge{\bf{\underline{\underline{\blue{To Find:}}}}}}$

Answer the following questions:

(a) How many trees did Ram’s orchard have initially?

(b) What is the total harvest produced if no tree is cut?

(c) If number of trees cut down decrease by 2 and each tree produced 6 apples more, then what is total harvest?

(d)If trees were 300 and total harvest 62,500, each tree producing 250 apples, then how

many trees were cut?

(e) Ram’s harvest depends on

(i) number of trees cut. (ii) apples produced by each tree.

_______________________

${\huge{\bf{\underline{\underline{\orange{Solution :}}}}}}$

(a.)Total no. of apples grown = 41,790

Apples grown on 1 tree = 210

${\sf{No. \: of \: trees = \frac{41790}{210} }}$

${\cancel{\red{ \frac{41790}{210} }}}{\blue{ = 199}}$

______________________

(b.)No. of trees cut = 5

If he had not cut no. of trees = 199 + 5 = 204

1 tree produced apples = 210

204 trees produced apples = 210 × 204

${\sf{\red{204 \times 210 = }}}{\blue{ \: 42840 }}$

______________________

(c.)If trees cut decreased by 2 = 5 - 2 = 3 + 199 = 202

If each tree could hold 6 apples more = 210 + 6 = 216

Than what will be the harvest = 202 × 216

${\sf{\red{202 \times 216 = }}}{\blue{ \: 43632}}$

______________________

(d.)If total no. of trees = 300

Total harvest = 62,500

Each tree produced = 250 apples

${\sf{Trees \: that \: gave \: 62500 \: apples= \frac{62500}{250} }}$

${\cancel{\red{ \frac{62500}{250} }}}{\blue{ = 250}}$

Trees cut = 300 - 250

${\sf{\red{300 - 250}}}{\blue{ \: = 50}}$

______________________

(e.)

${\sf{\red{Ram \: harvest \: depends \: on \: no. \: of \: apples \: produced \: by \: trees.}}}$

_______________________

${\large{\bf{\blue{\underline{\underline{Final \: Answers :}}}}}}$

${\bf{\orange{(a.)199 \: trees}}}$

${\bf{\orange{(b.)42,840 \: apples}}}$

${\bf{\orange{(c.)43,632 \: apples}}}$

${\bf{\orange{(d.)50 \: trees}}}$

${\bf{\orange{(e.)No. \: of \: apples \: produced \: by \: trees.}}}$

______________________

${\mathfrak{\green{XitzNobitaX}}}$