Aptitude Overflow

+2 votes

Month | Stage | Cost(Rs. '000 per man-month) |
---|---|---|

$1-2$ | Specification | $40$ |

$3-4$ | Design |
$20$ |

$5-8$ | Coding |
$10$ |

$9-10$ | Testing |
$15$ |

$11-15$ | Maintenance | $10$ |

The number of people employed in each month is:

Month | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ | $11$ | $12$ | $13$ | $14$ | $15$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

No. of people employed | $2$ | $3$ | $4$ | $3$ | $4$ | $5$ | $5$ | $4$ | $4$ | $1$ | $3$ | $3$ | $1$ | $1$ | $1$ |

Due to an overrun, the Design stage took three months, i.e. months $3, 4$ and $5$. The number of people working on Design in the fifth month was $5$. Calculate the percentage change in the cost incurred in the fifth month. (due to improvement in “Coding” technique, the stage was completed in months $6-8$ only).

- $225$%
- $150$%
- $275$%
- $240$%

0 votes

If the coding stage was performed in the $5^{th}$ month, then the cost will be $10,000 $ per man-month which is $10,000 \times 4 = 40,000$ because the coding stage was supposed to perform by $4$ people.

But,

now the design stage is performed in the $5^{th}$ month & $5$ people are working on that stage and for performing or doing the design stage the cost is $20,000$ per man-month, & the total cost will be $20,000 \times 5 = 1,00,000$ in the $5^{th}$ month.

In the $5^{th}$ month, the cost was supposed to be $40,000$

& now the cost incurred = $1,00,000$

Percentage change in the cost incurred in the $5^{th}$ month = $\dfrac{(1,00,000-40,000)}{40,000} \times 100\% \\ = \dfrac{60,000}{40,000} \times 100\% \\ = \dfrac{6}{4} \times 100\% \\ = \dfrac{3}{2} \times 100\% \\ = 150\%$

But,

now the design stage is performed in the $5^{th}$ month & $5$ people are working on that stage and for performing or doing the design stage the cost is $20,000$ per man-month, & the total cost will be $20,000 \times 5 = 1,00,000$ in the $5^{th}$ month.

In the $5^{th}$ month, the cost was supposed to be $40,000$

& now the cost incurred = $1,00,000$

Percentage change in the cost incurred in the $5^{th}$ month = $\dfrac{(1,00,000-40,000)}{40,000} \times 100\% \\ = \dfrac{60,000}{40,000} \times 100\% \\ = \dfrac{6}{4} \times 100\% \\ = \dfrac{3}{2} \times 100\% \\ = 150\%$

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