## [Speed Time Work] Two Men can finish a work, A is 3x more efficient than B, B leaves before completion & variety of cases

- Case: A & B work start together but B leaves
- Case: A started work, B joined after 4 days, how days work lasted?
- Case: A starts, B joins, How long did B work?
- Case: A and B start together but A leaves
- Case: Efficiency given: A is thrice good than B

# Case: A & B work start together but B leaves

Q.Kalmadi can build a stadium in 14 days, while Raja can do the same in 21 days. They started working together.

- Case #1: 3 days before the completion of work, Kalmadi was sent to Tihad jail. So find out Total Number of days to complete the work?
- Case #2: Same question but Raja goes to jail.

## Step 1: Draw the STD Table

Whether it is Pipes and Cistern problem or it is Time and Work problem, draw the “STD” table, fill up the values

Kalmadi | Raja | Kalmadi + Raja | |

Speed | |||

Time | 14 | 21 | |

Distance |

## Step 2: Take LCM, update Table

Now we’ll take the LCM of 14, 21

14=2×7

21=3×7

LCM (14,21)= 2x3x7=42

Let’s just visualize this stadium has just 42 seats. And these fine gentlemen have to place the seats, and drill the bolts.

So 42 seats is the “Total work to be done” or Total Distance to be covered.

Fill up the table

Kalmadi | Raja | Kalmadi + Raja | |

Speed | |||

Time | 14 | 21 | |

Distance | 42 | 42 |

Now the speed of Kalmadi

Sx T= D

S x 14=42 ; because we know Kalmadi takes 14 days to finish this work

Speed of Kalmadi= 42/14= 3 seats a day

Same way Raja can fit 2 seats a day (because 21 x 2 = 42)

Update the Table

Kalmadi | Raja | Kalmadi + Raja | |

Speed | 3 | 2 | |

Time | 14 | 21 | |

Distance | 42 | 42 |

## Step 3: Kalmadi + Raja Together?

What if Kalmadi + Raja work together? Obviously their speed will increase.

Now they can fit 3+2 = 5 seats per day.

Kalmadi | Raja | Kalmadi + Raja | |

Speed | 3 | 2 | 3+2=5 |

Time | 14 | 21 | ?? |

Distance | 42 | 42 | ?? |

BUT we don’t know for how many days did they work together?

So we cannot find how many seats they fixed. (STD formula requires two known values!)

So leave the (Kalmadi+Raja) column and move ahead.

## Step 4: Kamadi goes to Jail, Raja Works Alone

We are given that “3 days before the completion of work, Kalmadi was sent to Tihad jail.”

It means for the last three days, Raja worked alone, right ?

So, Expand the table, create one more column for Raja Alone

Kalmadi | Raja | Kalmadi + Raja | Raja alone | |

Speed | 3 | 2 | 3+2=5 | 2 |

Time | 14 | 21 | ?? | 3 |

Distance | 42 | 42 | ?? | 6 |

So, how many seats did Raja fix in last three days?

Speed x time = distance

2 x 3 = 6. ; Because Raja’s speed Is 2 and he works for 3 days.

## Step 5: Remaining seats

We know that total seats= 42, and Raja fixed 6.

Meaning 42 minus 6 = 36 seats were fixed by Kalmadi +Raja together.

Plug the value back in the Table

Kalmadi | Raja | Kalmadi + Raja | Raja alone | |

Speed | 3 | 2 | 3+2=5 | 2 |

Time | 14 | 21 | ?? | 3 |

Distance | 42 | 42 | 36 | 6 |

Again STD formula to find how many days did they work together ?

Speed (Kalmadi + Raja) x Time = Distance

5 x Time = 36

Time = 36/5=7.2

Thus, our final table looks like this

Kalmadi | Raja | Kalmadi + Raja | Raja alone | |

Speed | 3 | 2 | 3+2=5 | 2 |

Time | 14 | 21 | 7.2 | 3 |

Distance | 42 | 42 | 36 | 6 |

We’re about to solve the problem now.

What is the Total time taken by these two fine gentlemen of impeccable integrity, to build this stadium?