1. A and B together take 5 days to do work, B and C take 7 days to do the same, and A and C take 4 days to do it. Who among these will take the least time to do it alone?

**Given:**

A and B take 5 days

B and C take 7 days

A and C take 4 days

**Solution:**

LCM(5, 7, 4) = 140 let total work be 140 unit

**Time** | **Work** | **Efficiency** |

5 | 140 | 28 |

7 | 20 |

4 | 35 |

The efficiency of A, B, C are

⇒ 2(A + B + C) = 28 + 20 + 35 = 83

⇒ A + B + C = 83/2 = 41.5

⇒ A = (A + B + C) - (B + C) = 41.5 - 20 = 21.5

By the same process

⇒ B = 41.5 - 35 = 6.5

⇒ C = 41.5 - 28 = 13.5

⇒ Time(A) = 140/21.5 = 6.51

⇒ Time(B) = 140/6.5 = 21.54

⇒ Time(C) = 140/13.5 = 10.37

A took the least time to complete the work. So, A is the fastest.

**∴ A finishes fastest in 6.51 days.**