Difficult problems:
1. P and Q started a business investing Rs 85,000 and Rs 15,000 respectively.
In what ratio the profit earned after 2 years be divided between P and Q
respectively?
Sol:
85,000*2 : 15,000*2
17*2 : 3*2=34:6
2. A,B and C started a business by investing Rs 1,20,000, Rs 1,35,000 and
Rs 1,50,000.Find the share of each ,out of an annual profit of Rs 56,700?
Sol: Ratio of shares of A,B and C=Ratio of their investments
120,000:135,000:150,000
=8:9:10
A's share=Rs 56,700*(8/27)=Rs 16,800
B's share =Rs 56,700*(9/27)=Rs 18,900
C's share =Rs 56,700*(10/27)=Rs 21,000
3. 3 milkman A,B,C rented a pasture A grazed his 45 cows for 12 days
B grazed his 36 cows for 15 days and c 60 cows for 10 days.If b's
share of rent was Rs 540 What is the total rent?
Sol:
45*12:36*15:60*10
=9:9:10
9 parts is equal to Rs 540
then one part is equal to Rs 60
total rent=60*28=Rs 1680
4.Ramu and Krishna entered into a partnership with Rs 50,000
and Rs 60,000, after 4 months Ramu invested Rs 25,000 more
while Krishna withdraw Rs 20,000 . Find the share of Ramu in
the annual profit of Rs 289,000.
Sol: Ramu : Krishna=50,000*4+75,000*8:60,000*4+40,000*8
=10:7
Ramu's annual profit=289000*(10/17)=Rs 170,000
5.A,B,C enter into partnership .A invests 3 times as much as B invests
and B invests two third of what C invests. At the end of the year ,the
profit earned is Rs 6600. what is the share of B?
Sol:
let C's capital =Rs x
B's capital=Rs (2/3)*x
A's capital =3*(2/3)*x=Rs 2x
ratio of their capitals=2x:(2/3)*x:x
=6x:2x;3x
B's share =Rs 6600(2/11)=Rs 1200
6. A,B and C enter into a partnership by investing in the ratio of 3:2:4.
After one year ,B invests another Rs 2,70,000 and C,at the end of 2 years,
also invests Rs 2,70,000.At the end of 3 years ,profit are shared in the
ratio of 3:4:5.Find the initial investment of each?
Sol:
Initial investments of A,B,c be Rs 3x, Rs 2x, Rs 4x
then for 3 years
(3x*36):[(2x*12)+(2x+270000)*24]:[(4x*24)+(4x+270000)*12]=3:4:5
108x:(72x+640,000):(144x+3240000)=3:4:5
108x:72x+6480000:144x+3240000=3:4:5
(108x)/(72x+6480000)=3/4
432x=216x+19440000
216x=19440000
x=Rs 90000
A's initial investment=3x=3*90,000=Rs 2,70,000
B's initial investment=2x=2*90,000=Rs 1,80,000
C's initial investment=4x=4*90,000=Rs 3,60,000
