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Question

(i) A certain sum was divided among A, B and C in the ratio 7: 5: 4. If B got Rs 500 more than C, find the total sum divided.

(ii) In a business, A invests Rs 50000 for 6 months, B Rs 60000 for 4 months and C Rs 80000 for 5 months. If they together earn Rs 18800 find the share of each.


Solution

$$(i)$$ It is given that

Ratio between $$A, B$$ and $$C$$ = $$7: 5: 4$$

Consider,

$$A$$ share = $$7x$$

$$B$$ share = $$5x$$

$$C$$ share = $$4x$$

So the total sum =$$ 7x + 5x + 4x = 16x$$

Based on the condition

$$5x – 4x = 500$$

$$x = 500$$

So the total sum =$$ 16x = 16 \times 500 = Rs\ 8000$$



$$(ii)$$ $$1$$ months investment of $$A = Rs\ 50000$$

$$6$$ month investment of $$A = 50000 \times 6 = Rs\ 300000$$

$$1$$ months investment of $$B = Rs\ 60000$$

$$4$$ month investment of $$B = 60000 \times 4 = Rs\ 240000$$

$$1$$ months investment of $$C = Rs\ 80000$$

$$5$$ month investment of $$C = 80000 \times 5 = Rs\ 400000$$

Here the ratio between their investments = $$300000: 240000: 400000= 30: 24: 40$$

Sum of ratio = $$30 = 24 + 40 = 94$$

Total earnings = $$Rs\ 18800$$

So we get share of earning by each as ,

$$A$$ share = $$\cfrac{30}{94} \times 18800 = Rs\ 6000$$

$$B$$ share = $$\cfrac{24}{94}\times 18800 = Rs\ 4800$$

$$C$$ share = $$\cfrac{40}{94} \times 18800 = Rs\ 8000$$

Maths

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