Aptitude Discussion

Q. |
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). |

✖ A. |
20 |

✖ B. |
40 |

✖ C. |
45 |

✔ D. |
77 |

**Solution:**

Option(**D**) is correct

Let us first consider a general series,

$=[1+ (1+2)+(1+2+3)+ ..... +(1+2+3+....+n)]$

Sum of above series for $n$ terms,

$=\dfrac{n(n+1)(n+2)}{6}$

⇒ The number of boys-days

\(=\dfrac{1}{6}[1+ (1+2)+(1+2+3)+ ..... +(1+2+3+....+20)]\)

\(=\dfrac{20\times 21\times 22}{6}\)

$= 1540$

⇒ But, each boy \(=1/2 \) girls \(\Rightarrow 770\) girl-days.

⇒ 10 girls will take \(770/10 = \textbf{77 days.}\)

**Edit:** Thank you, **Bhavya Shah**, for letting us know the error, formula to the given series ie added and typo in mentioning the sum of the series is corrected.

**Karthick**

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**Gourab Mukherjee**

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How was the sum of the series calculated? Can Anyone plz explain

**Sakshi**

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on the second day abhishek is assisted by 2 more frnds, which means that on second day 3 people have worked. then why does the second term of the series contain only two sub-terms? i mean it should be....

1+ (1+2+3)+ (1+2+3+4+5+6)+........... so on....

Please explain

**Bhavya Shah**

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Formula is $\dfrac{n(n+1)(n+2)}{6}$

And the sum turns out to be 1540 instead of 1440

Thank you, Bhavya, corrected the typo and mentioned the formula to the sum of the series in solution.

**Shivani**

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In this, how sum of series is calculated?

Why we multiply with (1/6) and also the formula to find the number of boys and their days used for their jobs...!???