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Question

$$A$$ can do a job in $$10$$ days while $$B$$ can do it in $$15$$ days. If they work together and earn $$₹3500$$, how should they share the money?


Solution

Given,
$$A$$ can do a job in = $$10$$ days
So, $$A$$’s $$1$$ day's job is = $$\dfrac1{10}$$

$$B$$ can do a job in $$15$$ days
So, $$B$$’s $$1$$ day job is $$= \dfrac1{15}$$

Job done by both $$A$$ and $$B$$ in one day $$= \dfrac1{10} + \dfrac1{15}$$
$$= \dfrac{3+2}{30}= \dfrac 5{30}=\dfrac 16$$

For $$\dfrac 16$$ part of work the earnings is = $$₹3500$$
So, for $$1$$ part of work the earnings is = $$₹3500 \times 6$$

Therefore,
For $$\dfrac1{10}$$ part of work earning = $$₹\ \dfrac{3500 \times 6}{10} = ₹2100$$
For $$\dfrac1{15}$$ part of work earning = $$₹\ \dfrac{3500 \times 6}{15} = ₹1400$$

$$\therefore$$ $$A$$ gets $$₹2100$$ and $$B$$ gets $$₹ 1400$$


Mathematics

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