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A certain amount of money was divided in the ratio 2:3:5. If the difference between the largest share and the smallest share was 7,500 Shillings, find the largest share.

Mathematics

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Answer

E) 12,500 /=\text{E) 12,500 /=}

Step-by-step solution

4 steps

  1. Identify the ratio parts for the smallest and largest shares.

    The money is divided in the ratio $2:3:5$.
    The smallest share corresponds to 2 parts.
    The largest share corresponds to 5 parts.

  2. Calculate the difference in ratio parts between the largest and smallest shares.

    Difference in parts = Largest part - Smallest part

    Difference in parts=5−2=3 parts\text{Difference in parts} = 5 - 2 = 3 \text{ parts}

  3. Use the given monetary difference to find the value of one ratio part.

    We are told that the difference between the largest and smallest share is 7,500 Shillings.
    So, 3 parts = 7,500 Shillings.
    To find the value of 1 part:

    1 part=75003=2500 Shillings1 \text{ part} = \frac{7500}{3} = 2500 \text{ Shillings}

  4. Calculate the largest share.

    The largest share corresponds to 5 parts.

    Largest share=5×2500=12500 Shillings\text{Largest share} = 5 \times 2500 = 12500 \text{ Shillings}

    The final answer is E) 12,500 /=\text{E) 12,500 /=}.

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