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Exercise 7 · Q8

Q.Arun started a business investing ₹38000. After 5 months Bakul joined him with a capital of ₹55000. At the end of the year the total profit was ₹22000. What is the approximate difference between the shares of Arun and Bakul?

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Capital×time: Arun 456000456000, Bakul 385000385000 (ratio 456:385456:385, sum 841841); the difference =71841×22000≈=\dfrac{71}{841}\times22000\approx ₹1857.

Profit shared in ratio of (Capital×Months)(\text{Capital}\times\text{Months}); Difference=∣CAtA−CBtB∣CAtA+CBtB×Profit\text{Difference}=\dfrac{|C_A t_A-C_B t_B|}{C_A t_A+C_B t_B}\times\text{Profit}.

  1. Arun invests 2˘0b938000\u20b938000 for 12 months: 38000×12=45600038000\times12=456000.
  2. Bakul joins after 5 months, so he invests 2˘0b955000\u20b955000 for 12−5=712-5=7 months: 55000×7=38500055000\times7=385000.
  3. Ratio Arun : Bakul =456000:385000=456:385=456000:385000=456:385; total parts =456+385=841=456+385=841.
  4. Arun's share =456841×22000≈2˘0b911928.66=\dfrac{456}{841}\times22000\approx\u20b911928.66; Bakul's share =385841×22000≈2˘0b910071.34=\dfrac{385}{841}\times22000\approx\u20b910071.34. …

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