Math Problem Statement

A is twice as good as workman as B and together they finish a piece of work in 14 days. In how many days can A alone finish the work? A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. The number of days taken by B to finish the work is : A and B can do a piece of work in 45 and 40 days respectively. They began the work together but A leaves after some days and B finished the remaining work in 23 days. After how many days did A leave?

Solution

This image presents three mathematical word problems related to work and time:

Q.11:

  • A is twice as good a worker as B, and together they can finish a piece of work in 14 days. How many days will it take for A alone to finish the work?

Q.12:

  • A is thrice as good a worker as B and takes 10 days less to do a piece of work than B. The number of days taken by B to finish the work is?

Q.13:

  • A and B can finish a piece of work in 45 and 40 days, respectively. They began the work together, but A left after some days, and B finished the remaining work in 23 days. After how many days did A leave?

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Math Problem Analysis

Mathematical Concepts

Work and Time
Rates of Work
Time Management

Formulas

Work done = 1 / Time taken
Time taken by A and B working together = (AB) / (A + B)

Theorems

Rates of Work Theorem

Suitable Grade Level

Grades 7-10