High School

1. A and B together can finish a job in 10 hours. A alone can do the same job in 15 hours. If A and B start working together but A leaves after 4 hours, how much longer will B need to finish the remaining work?
Options: A. 12 hours B. 23 hours C. 18 hours D. 10 hours

2. Robert is travelling on his cycle and has calculated to reach point A at 3 PM if he travels at 20 kmph, and he will reach there at noon, if he travels at 25 kmph. At what speed must he travel to reach A at 2 P.M.?
Options: A. 24.44 km/h B. 18.25 km/h C. 21.43 km/hr. D. 28.42 km/h

3. In a factory of T-shirt making, 4%, 5%, 10%, 20% and 12.5% pieces are made defective from 300, 500, 230, 30 and 480 pieces respectively which are made every day from Monday to Friday. What is the percentage of defective T-shirts out of the total T-shirts made?
Options: A. 10% B. 7.4% C. 8.18% D. 6.4%

4. Rambo has taken a loan of 40000 USD from Bank of America at 15% per annum compounded annually. At the end of the first year, he paid USD 10000 and at the end of the second year, he wanted to clear the loan. How much should he pay in order to settle his loan?
Options: A. USD 41400 B. USD 40000

Answer :

Let's solve each question step by step.

  1. Calculating Time B Needs to Finish the Job

    • Total work rate of A and B together:
      [tex]\text{Work rate of A and B} = \frac{1}{10} \text{ of the job per hour}[/tex]

    • Work rate of A alone:
      [tex]\text{Work rate of A} = \frac{1}{15} \text{ of the job per hour}[/tex]

    • Work rate of B alone:
      Since A and B together complete [tex]\frac{1}{10}[/tex] of the job in an hour and A alone completes [tex]\frac{1}{15}[/tex] in an hour, we find B's rate by subtracting A's rate from the combined rate:
      [tex]\text{Work rate of B} = \frac{1}{10} - \frac{1}{15} = \frac{1}{30} \text{ of the job per hour}[/tex]

    • Amount of work done by A in 4 hours:
      [tex]\text{Work done by A in 4 hours} = 4 \times \frac{1}{15} = \frac{4}{15}[/tex]

    • Remaining work after A leaves:
      The total work remaining for B will be:
      [tex]1 - \frac{4}{15} = \frac{11}{15}[/tex]

    • Time B needs to finish the remaining work:
      [tex]\text{Time for B to finish} = \frac{\text{Remaining work}}{\text{Work rate of B}} = \frac{\frac{11}{15}}{\frac{1}{30}} = 22 \text{ hours}[/tex]

    The closest option based on provided choices given the calculated result is not listed accurately (just an estimation). However, the answer does not match any options exactly.

  2. Calculating Robert's Speed to Reach by 2 PM

    • Time difference between speeds:
      If Robert's time changes based on his speed from reaching at 3 PM to noon, the time difference is 3 hours.

    • Calculating Distance:
      Let the distance be [tex]D[/tex]. Using speed and time difference:
      [tex]\frac{D}{20} - \frac{D}{25} = 3[/tex]

      Solving for [tex]D[/tex]:
      [tex]D = \frac{20 \times 25 \times 3}{25 - 20} = 300 \text{ km}[/tex]

    • Calculating Speed to Arrive by 2 PM:
      If Robert travels to cover the same distance by 2 PM:

      • Time taken from noon to 2 PM is 2 hours, thus:
        [tex]\frac{300}{\text{Speed}} = 15[/tex] (travelling from earlier start for 5 total hours)

      Therefore, speed:
      [tex]\text{Speed} = \frac{300}{15} = 20 \text{ km/h}[/tex]

    The correct speed to reach at 2 PM was listed correctly as 24.44 km/h, however, since the actual calculation is incorrect to choose: (A. NOT included)

  3. Calculating Percentage of Defective T-Shirts

    • Calculating Defective T-Shirts:

      • Monday: [tex]4\%[/tex] of 300 = 12
      • Tuesday: [tex]5\%[/tex] of 500 = 25
      • Wednesday: [tex]10\%[/tex] of 230 = 23
      • Thursday: [tex]20\%[/tex] of 30 = 6
      • Friday: [tex]12.5\%[/tex] of 480 = 60

    • Total Defective T-Shirts: 126
      [tex]\text{Total made} = 300 + 500 + 230 + 30 + 480 = 1540[/tex]

    • Percentage of Defective T-Shirts:
      [tex]\frac{126}{1540} \times 100 \approx 8.18\%[/tex]

    The correct option is C. 8.18%.

  4. Calculating Amount Rambo Needs to Pay at the End of the Second Year

    • End of First Year Calculation:

      • Principal at start: $40,000
      • Amount after interest for one year: [tex]40000 \times 1.15 = 46,000[/tex]
      • Remaining after paying $10,000 = 46,000 - 10,000 = 36,000

    • End of Second Year Calculation:

      • New principal amount: 36,000
      • Amount after interest for second year: [tex]36,000 \times 1.15 = 41,400[/tex]

    Therefore, Rambo would need to pay A. USD 41,400 to settle the loan.

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