Question

A certain group of teenagers came together and decided to turn barren land into a mini forest. Their first step was to plant many saplings in the piece of land. They decided to plant 126 saplings in a set number of days. In the initial five days, they planted as many saplings as they had planned for each day. For the rest of the days, they were able to plant six more saplings than their actual target. So, they could plant 1986 saplings a day before their planned last day. What was the number of saplings the group had planned to plant every day?​

Answer 1

Answer 1) :-

Let us assume that, they planned to plant saplings for total x days.

now,

→ Saplings in 1 day = ( 126 /x )

so ,

→ in 5 days saplings they plant = 5(126/x) = (630/x)

now,

Days left = (x - 5)

and,

→ For rest days saplings they plant = (126/x) + 6 .

then,

→ Total saplings in (x - 6) days = (x - 6) * {(126 + 6x)/x} [ Before 1 day. ]

A/q,

→ (630/x) + [(x - 6) * {(126 + 6x)/x}] = 1986

→ [630 + (x - 6)(126 + 6x)] = 1986x

→ 630 + 126x + 6x² - 756 - 36x = 1986x

→ 6x² + 90x - 126 = 1986x

→ 6x² - 1896x - 126 = 0

→ 6(x² - 316x - 21) = 0

→ x² - 316x - 21 = 0

solving this we get,

→ x = (±√24985 + 158)

→ x ≈ 0.6 , 316 .

since x can not be equal to 0.6 days.

now, if we take,

→ x = 316 days .

→ The number of saplings the group had planned to plant every day :-

→ 5*x + 310*6 = 1986

→ 5x = 1986 - 1860

→ 5x = 126

→ x ≈ 25 saplings (Ans.)

Answer 2) :-

if it is given that, initially they plant 126 saplings per day for 5 days and then, six more saplings their actual target. So, they could plant 1986 saplings a day before their planned last day. What was the number of days the group had planned to plant saplings ?

in this case let total days the planned to plant saplings is let x .

so,

→ 126 * 5 + (126 + 6)(x - 6) = 1986

→ 630 + 132x - 792 = 1986

→ 132x - 162 = 1986

→ 132x = 1986 + 162

→ 132x = 2148

→ x ≈ 17 days. (Ans.)

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