Question

Abhishek starts to paint a fence on one day. On the second day, two more friend of Abhishek join him.
On the third day 3 more friends of him join him and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 girls painting together can paint the fence completely, given that every girl can paint twice as fast as Abhishek and his friends(Boys)?
(Assume that the friends of Abhishek are all boys).
Need solution​

Answer 1

Given :- Abhishek starts to paint a fence on one day. On the second day, two more friend of Abhishek join him. On the third day 3 more friends of him join him and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 girls painting together can paint the fence completely, given that every girl can paint twice as fast as Abhishek and his friends(Boys) ? (Assume that the friends of Abhishek are all boys).

Solution :-

given that, the friends of Abhishek are all boys .

Let us assume that, Efficiency of each boys is 1m . ( Each boys paint 1 m area fence per day. )

Than,

→ On first day abhishek paint area = 1m .

→ On second day (abhishek + 2 boys) paint area = 3*1 = 3m .

→ On 3rd day (abhishek + 3 boys) paint area = 4*1 = 4m .

→ On 4th day (abhishek + 4 boys) paint area = 5*1 = 5m .

So on ____________

and,

→ On 20th day , (abhishek + 20 boys) paint area = 21*1 = 21m .

Therefore,

→ Total area painted in 20 days is = 1 + 3 + 4 + 5 + _____________ 21 . = 1 + (3 + 4 + 5 + ________ 21) = 1 + [(19/2)(2*3 + 18*1)] = 1 + [(19/2) * 24] = 1 + (19 * 12) = 1 + 228 = 229m . = Total Area of Fence . { Using AP sum formula.}

Now, this area is to be painted by 10 girls together and every girl can paint twice as fast as Abhishek and his friends(Boys) .

So,

→ Each girl paint area per day = 2 * boy = 2 * 1 = 2m.

Than,

→ 10 girls together paint area per day = 2 * 10 = 20m.

Hence,

→ Time taken by girls to paint total area of fence = (Total area) / (per day they paint) = 229/20 = 11.45 days. (Ans.)

∴ 10 girls together can paint the fence in 11.45 days..

(Excellent question.)

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