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A and B undertaken to do a piece of work for Rs.1200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days, Find C's share.

Correct Answer:

A) Rs.450 |
B) Rs.300 |

C) Rs.150 |
D) Rs.100 |

Correct Answer:

C) Rs.150 |

Description for Correct answer:

According to the question,

\( \Large \frac{1}{A} \)+\( \Large \frac{1}{B} \)+\( \Large \frac{1}{C} \) = \( \Large \frac{1}{3} \)

= \( \Large \frac{1}{8} \)+\( \Large \frac{1}{6} \)+\( \Large \frac{1}{C} \) = \( \Large \frac{1}{3} \)

= \( \Large \frac{1}{C}=\frac{1}{3}- \left(\frac{1}{8}+\frac{1}{6}\right)=\frac{1}{24} \)

Therefore, Ratio in shares of A, B and C = \( \Large \frac{1}{8} \) : \( \Large \frac{1}{6} \) : \( \Large \frac{1}{24} \)

= \( \Large \frac{3}{24} \) : \( \Large \frac{4}{24} \) : \( \Large \frac{1}{24} \) = 3 : 4 : 1

Therefore, C's share = \( \Large \frac{1}{3+4+1} \times 1200 \) = Rs.150

According to the question,

\( \Large \frac{1}{A} \)+\( \Large \frac{1}{B} \)+\( \Large \frac{1}{C} \) = \( \Large \frac{1}{3} \)

= \( \Large \frac{1}{8} \)+\( \Large \frac{1}{6} \)+\( \Large \frac{1}{C} \) = \( \Large \frac{1}{3} \)

= \( \Large \frac{1}{C}=\frac{1}{3}- \left(\frac{1}{8}+\frac{1}{6}\right)=\frac{1}{24} \)

Therefore, Ratio in shares of A, B and C = \( \Large \frac{1}{8} \) : \( \Large \frac{1}{6} \) : \( \Large \frac{1}{24} \)

= \( \Large \frac{3}{24} \) : \( \Large \frac{4}{24} \) : \( \Large \frac{1}{24} \) = 3 : 4 : 1

Therefore, C's share = \( \Large \frac{1}{3+4+1} \times 1200 \) = Rs.150

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