Answer:
Mohan lent 3600 to Ram and 3000 to Shyam.
Step-by-step explanation:
Given that Mohan lent altogether 6,600 to Ram and Shyam for 2 years.
Let Mohan lent x to Ram and y to Shyam
x+y=6600
Or, x=6600-y ...(i)
As Ram pays simple interest at 15 %=0.15 p.a, so, the interest paid by Ram in 2 years:
[tex]I=x\times 0.15 \times 2 \\\\\Rightarrow I=0.3x \\\\[/tex]
[tex]\Rightarrow I=0.3(6600-y) \\\\[/tex] [by using (i)]
[tex]\Rightarrow I=1980-0.3y \cdots(ii)[/tex]
As Shyam pays compound interest at 15 %=0.15 p.a,
so, the interest paid by Shyam in 2 years, C.I.= Final amount - Initial principal amount
[tex]C.I. = y(1+0.15)^2-y \\\\\Rightarrow C.I. = y(1.15^2-1) \\\\\Rightarrow C.I. = y(1.3225-1) \\\\\Rightarrow C.I. = 0.3225y \cdots(iii)[/tex]
As Ram paid Rs 112.50 more than Shyam as the interest, so by using equations (ii) and (iii),
[tex](1980-0.3y)-0.3225y=112.5 \\\\\Rightarrow 1980-0.3y-0.3225y=112.5 \\\\\Rightarrow 0.6225y=1980-112.5 \\\\\Rightarrow y = 1867.5/0.6225=3000[/tex]
From equations (i),
[tex]x=6600-3000=3600[/tex]
Hence, Mohan lent 3600 to Ram and 3000 to Shyam.
