A person invested a total sum of Rs. 15,500 in three different schemes of simple interest at the annual rate of 4 percent, 6 percent and 10 percent. At the end of one year he got same interest in all three schemes. What is the sum invested at the rate of 6 percent ?

Rs. 5000

Total Sum = Rs 15500

15500 is invested into 3 different schemes i.e. at 4%, 6% and 10% p.a. respectively for 1 year

P1 = x , P2 = y , P3 = z (P=Principal)

ATQ,

I1=I2=I3

\(\frac{P1×R1×T1}{100}\) = \(\frac{P2×R2×T2}{100}\) = \(\frac{P3×R3×T3}{100}\)

\(\frac{x×4×1}{100}\) = \(\frac{y×6×1}{100}\) = \(\frac{z×10×1}{100}\)

4x = 6y = 10z

∴ \(\frac{x}{15}\) = \(\frac{y}{10}\) = \(\frac{z}{6}\)

ATQ

P1+P2+P3 = 15500

15+10+6 = 15500

31 part = 15500

1 part = 500

Sum invested at 6% pa = 10 part

1 = 500

100  = 10 × 500

       = Rs 5000