A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?

Question: A and B enter into a partnership. A invest Tk 5000. At the end of 3 months, he withdraws Tk 500 and at the end of 7 months he withdraws another Tk 900. B gets Tk 800 as his share of the total profit of Tk 1800 at the end of the year. How much did B invest, if B invested along with A at the beginning of the year?

Solution:
A invest 5000 for 3 months, 4500 for 4 months and 3600 for 5 months and gets a interest of 1000

ATQ,
{(5000 × R × 3)/(12 × 100)} + {(4500 × R × 4)/(12 × 100)} + {(3600 × R × 5)/(12 × 100)} = 1000
⇒ {(15000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} + {(18000 × R)/(12 × 100)} = 1000
⇒ (15000R/1200) + (18000R/1200) + (18000R/1200) = 1000
⇒ (51000R)/1200 = 1000
⇒ 51000R = 1200000
⇒ R = 1200000/51000
⇒ R=1200/51

For B,
{(P × 1200)/(51 × 1)}/100 = 800
⇒ (P × 1200/51)/100 = 800
⇒ (P × 1200)/51 = 80000
⇒ P × 1200 = 4080000
∴ P = 3400