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1. 3 men complete a work in 6 hours. In how many hours will 12 men complete the same work?

2. If a 25 cm long candle burns for 45 minutes, how long will another candle of the same material and same thickness but 5 cm longer than the previous one burn?

3. A typist takes 80 minutes to type 24 pages. How long will he take to type 87 pages?

4. ₹ 750 supports a person for 15 days. For how many days will ₹ 2,500 support the same person?

Answer :

Let's tackle each question step-by-step:

  1. Work Distribution:

    We know that 3 men complete a work in 6 hours. The work done is the same, so we can use proportions to find out how long it will take 12 men.

    First, we calculate the total work done by the 3 men:

    [tex]\text{Work} = 3 \text{ men} \times 6 \text{ hours} = 18 \text{ man-hours}[/tex]

    Now, we divide this same amount of work by 12 men:

    [tex]\text{Time} = \frac{18 \text{ man-hours}}{12 \text{ men}} = 1.5 \text{ hours}[/tex]

    So, 12 men will complete the work in 1.5 hours.

  2. Candle Burning:

    A 25 cm long candle burns for 45 minutes. We need to find out how long a 30 cm candle will burn.

    If the candle burns uniformly, then the time taken is directly proportional to the length of the candle:

    [tex]\text{Time ratio} = \frac{30 \text{ cm}}{25 \text{ cm}} = 1.2[/tex]

    Burning time for the 30 cm candle:

    [tex]45 \text{ minutes} \times 1.2 = 54 \text{ minutes}[/tex]

    Hence, the 30 cm candle will burn for 54 minutes.

  3. Typing Pages:

    The typist takes 80 minutes to type 24 pages. We want to find out how long he will take to type 87 pages.

    First, find the typing speed in minutes per page:

    [tex]\text{Speed} = \frac{80 \text{ minutes}}{24 \text{ pages}} \approx 3.33 \text{ minutes/page}[/tex]

    Now, multiply this by the number of pages to be typed:

    [tex]\text{Time} = 87 \text{ pages} \times 3.33 \text{ minutes/page} \approx 289.71 \text{ minutes}[/tex]

    So, it will take approximately 290 minutes to type 87 pages.

  4. Budget Support:

    If ₹ 750 supports a person for 15 days, we need to determine how many days ₹ 2,500 will provide support.

    Calculate the cost per day first:

    [tex]\text{Cost per day} = \frac{750}{15} = 50 \text{ rupees/day}[/tex]

    Now find out the number of days ₹ 2,500 will last:

    [tex]\text{Days} = \frac{2500}{50} = 50 \text{ days}[/tex]

    Therefore, ₹ 2,500 will support the person for 50 days.

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