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In a colony of 60 people, the language spoken by each person is noted. 10 speak only Bengali, 5 speak only Assamese, 10 speak Hindi and Odia, 12 speak Marathi and Hindi, 13 speak English, Tamil and Ma

Mathematics

ScanSolve AI Answer

Answer

D

Step-by-step solution

6 steps
  1. Calculate the number of people in each category.

    Total people in the colony = 60.

    • Only Bengali speakers = 10
    • Only Assamese speakers = 5
    • Hindi and Odia speakers = 10
    • Marathi and Hindi speakers = 12
    • English, Tamil, and Marathi speakers = 13
    • Assamese and Hindi speakers = 5
  2. Calculate the number of remaining people.

    Sum of people in known categories = 10+5+10+12+13+5=5510 + 5 + 10 + 12 + 13 + 5 = 55.
    The remaining people speak both Bengali and Hindi.
    Remaining people = Total people - Sum of known categories
    Remaining people = 60−55=560 - 55 = 5.
    So, Bengali and Hindi speakers = 5.

  3. Calculate the total number of Bengali speakers.

    Bengali speakers include those who speak only Bengali and those who speak Bengali and Hindi.
    Total Bengali speakers = (Only Bengali speakers) + (Bengali and Hindi speakers)
    Total Bengali speakers = 10+5=1510 + 5 = 15.

  4. Calculate the total number of Marathi speakers.

    Marathi speakers include those who speak Marathi and Hindi, and those who speak English, Tamil, and Marathi.
    Total Marathi speakers = (Marathi and Hindi speakers) + (English, Tamil, and Marathi speakers)
    Total Marathi speakers = 12+13=2512 + 13 = 25.

  5. Determine the ratio of Bengali speakers to Marathi speakers.

    Ratio = (Total Bengali speakers) : (Total Marathi speakers)
    Ratio = $15 : 25$.

  6. Simplify the ratio.

    Divide both numbers by their greatest common divisor, which is 5.
    Ratio = 155:255=3:5\frac{15}{5} : \frac{25}{5} = 3 : 5.

    The ratio of Bengali speakers to Marathi speakers is 3:53 : 5.

    The correct option is (D).

    D\boxed{\text{D}}

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