Question 12
Solve (Do not enter the unit "Rs." in the answer)
Kishore and Keerthi started a project with their respective Investments in the ratio of
4:5. After the project started, Sylaja and Sachin also joined with Investments in the ratio
of 3:2. If at the end of the year, Sylaja's share of the total profit amount was Rs.4000
more than that of Keerthi and 65% more than that of Kishore, then what was Sachin's
share of the total profit amount?
Answers
Given : Kishore and Keerthi started a project with their respective Investments in the ratio of 4:5. After the project started, Sylaja and Sachin also joined with Investments in the ratio
of 3:2. If at the end of the year, Sylaja's share of the total profit amount was Rs.4000 more than that of Keerthi and 65% more than that of Kishore,
To Find : Sachin's share of the total profit amount
Solution:
Kishore and Keerthi started a project with their respective Investments in the ratio of 4:5
Kishore investment = 4m
Keerti investment = 5m
Sylaja and Sachin also joined with Investments in the ratio of 3:2
Sylaja investment = 3n
Sachin investment = 2n
Total investment = 4m + 5m + 3n + 2n
= 9m + 5n
Let say total profit = A
Sylaja's share = A (3n)/(9m + 5n)
Keerthi sahre =A (5m) / (9m + 5n)
=> A (3n)/(9m + 5n) = A(5m) / (9m + 5n) + 4000
=> 3nA = 5mA + 4000 ( 9m + 5n)
=> 3nA = 5mA + 36000m + 20000n
=> n (3A - 20000 ) = 5m(A + 7200)
Kishore sahre =A (4m) / (9m + 5n)
A (3n)/(9m + 5n) ={A (4m) / (9m + 5n) }( 1 + 65/100)
=> A (3n)/(9m + 5n) = (1.65) A (4m) / (9m + 5n)
=> 3n = 6.6m
=> n = 2.2m
n (3A - 20000 ) = 5m(A + 7200)
=> 2,2m (3A - 20000 ) = 5m(A + 7200)
=> 6.6A - 44000 = 5A + 36000
=> 1.6A = 80000
=> A = 50000
Sachin share = A (2n) / ( 9m + 5n)
= 50000 * 2 * 2.2m / (9m + 11m)
= 220000m/20m
= 11000
Sachin's share of the total profit amount = 11000 Rs
Sylaja's share = A (3n)/(9m + 5n) = 50000(3*2.2m)/(9m + 5(2.2)m) = 16500
Keerthi sahre =A (5m) / (9m + 5n) = 12500
Kishore share =A (4m) / (9m + 5n) = 10000
Verification :
16500 = 12500 + 4000 Sylaja's share of the total profit amount was Rs.4000 more than that of Keerthi
10000 + (65/100)10000 = 165000 65% more than that of Kishore,
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Answer :-
we know that, Profit is distributed in the ratio of their investment .
So,
→ Profit of Sylaja = 65% more than that of Kishore .
→ Profit of Sylaja = (165/100) Kishor
→ Investment by Sylaja / Investment by Kishore = 33/20
→ Sylaja : Kishore = 33 : 20 .
now, we have,
- Kishore : Keerthi = 4 : 5
- Sylaja : Sachin = 3 : 2
- Sylaja : Kishore = 33 : 20 .
Making ratio same we get,
- Kishore : Keerthi = (4 : 5)*5 = 20 : 25
- Sylaja : Sachin = (3 : 2)*11 = 33 : 22
- Sylaja : Kishore = 33 : 20
then,
→ Kishore : Keerthi : Sylaja : Sachin = 20 : 25 : 33 : 22 .
given that,
→ Sylaja share - Keerthi share = 4000
→ 33 - 25 = 4000
→ 8 = 4000
→ 1 = 500
then,
→ Sachin share = 22 => 22 * 500 = Rs.11000 (Ans.)
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