Question

30 girls can finish a work in 40 days. Aftert how many days should 10 girls leave the work so that it may be finished in 46 days, if all the 30 girls started the work? (a) 18 days (b) 28 days (c) 22 days (d) 30 days

Short answer

Answer: 28 days.

Step-by-step solution

Analyze the given situation to set up the equation.

Let's denote the total work done as W. Since 30 girls can finish it in 40 days, we can say that: 30 girls × 40 days = W

Express the work situations in terms of girls and days.

Let x be the number of days after which the 10 girls leave the work. Thus, for x days, all the 30 girls will work together, and in the remaining (46 - x) days, 20 girls will continue the work. So we can set up the equation as follows: (30 girls × x days) + (20 girls × (46 - x) days) = W

Substitute the total work done from step 1.

Now, we know from step 1 that W = 30 girls × 40 days, so we substitute this expression into the equation we derived in step 2: (30 girls × x days) + (20 girls × (46 - x) days) = 30 girls × 40 days

Simplify and solve the equation.

Now, we can simplify the equation and solve for x: 30x + 20(46 - x) = 30 * 40 30x + 920 - 20x = 1200 10x = 280 x = 28 So, after 28 days, 10 girls should leave the work to finish it in 46 days. The answer is (b) 28 days.

Key concepts

Quantitative Aptitude

Quantitative aptitude is a measure of an individual's numerical and problem-solving abilities which is essential across various competitive exams and activities. It involves the application of mathematical concepts to solve real-world problems, similar to the textbook example provided.

In the given scenario, we must calculate the time at which a portion of a group should cease participation in a task to meet a specific deadline. This requires the understanding of basic arithmetic operations and the capability to translate a word problem into an algebraic expression. Problems like these not only enhance your quantitative skills but also prepare you for scenarios that require time management, resource allocation, and strategic planning.

Math Problem Solving

Math problem solving is a critical thinking process involving several steps to transition from a problem statement to a solution. Here's how we applied that process in our example:

• Understanding the problem: We first identify the goal—in this case, determining when 10 girls should leave the work to maintain a schedule.
• Devising a plan: The plan includes setting up an equation based on the given information.
• Carrying out the plan: We execute the plan by substituting known values into the equation.
• Looking back: Finally, we verify our solution to ensure it makes sense within the context of the problem.

Through regular exposure to such problems, students can sharpen their analytical skills and develop a systematic approach to tackling diverse challenges.

Equation Setup and Simplification

The ability to set up and simplify equations is a fundamental skill in math problem solving. Here's how the exercise demonstrates this vital technique:

We firstly recognized that we needed to express the total amount of work done, represented by variable W. The challenge is then broken down into two phases: one where all 30 girls work and another where only 20 girls continue. The equation reflects those two phases, with the unknown variable representing the change.

During simplification, we eliminate variables and numbers that don't serve in finding the solution, which leads to a more straightforward equation. In our case, after combining like terms and bringing constants to one side, we isolated the variable x. Simplification is crucial as it transforms complex statements into simpler forms which are easier to solve and understand. Through practice, equation simplification becomes an intuitive part of problem-solving, streamlining the journey from question to answer.