On 1st January 2020, Rekha invested an amount 'a' to start a business. After some months,Nisha joined her, investing an amount 'b'. Rekha and Nisha divided up the entire profit atthe end of 2020, in the ratio 6:5. At some point during 2021, they were joined by Nehawho invested an amount 'c'. At the end of 2021, Rekha, Nisha and Neha shared the entireprofit for that year in the ratio 4: 5: 2. At some point during 2022, Nisha left to pursuean MBA. Simultaneously, Radhika joined the company investing an amount 'd'. At the end of2022, Rekha, Nisha, Neha and Radhika shared the entire profit for that year in the ratio 65:12 : 3.For how many months was Nisha a nart of the business?
Answers
Solution :-
Let Nisha invest in 2020 for x months .
so,
→ 12a : xb = 6 : 5
→ 2a : xb = 1 : 5
→ 2a/xb = 1/5
→ (a/b) = (x/10) -------- Eqn.(1)
In 2021 let neha joined for y months .
so,
→ 12a : 12b : yc = 4 : 5 : 2
→ (12a/12b) = (4/5)
→ (a/b) = (4/5) -------- Eqn.(2)
comparing Eqn.(1) and Eqn.(2),
→ (x/10) = (4/5)
→ x = 8 months .
In 2022 let nisha left after z months and simultaneously, Radhika joined the company .
so,
→ 12a : zb : 12c : (12 - z)d = 6 : 5 : 12 : 3
→ (12a/zb) = (6/5)
→ (2a /zb) = (1/5)
→ (a/b) = (z/10) -------- Eqn.(3)
comparing Eqn.(1) and Eqn.(3),
→ (z/10) = (4/5)
→ z = 8 months .
therefore,
→ Nisha was part of the business for = 8 months + 12 months(2021) + 8 months = 28 months (Ans.)
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