Question

In any month, Harish deposits m% and withdraws
n% of the closing balance of the previous month. If his
balance at the end of March (after the withdrawal) is er
the same as his balance at the beginning of January one
(before the deposit), which of the following is true?
M
(A) n÷2<m<n (B) m=n
(C) m>n
(D) m<n÷2​

Answer 1

Answer:

B

Step-by-step explanation:

January

Deposit = m% of closing balance of December

= xm/100

Balance = x+xm/100

Withdrawal = n% of closing balance of December

=xn/100

Hence Closing Balance at the end of January = x + xm/100 - xn/100

= x[1+0.01m-0.01n]

Let 1+0.01m-0.01n =A

Closing Balance at the end of January = xA

February

Deposit = m% of closing balance of January

= xAm/100

Balance = xA + xAm/100

Withdrawal = n% of closing balance of January

= xAn/100

Hence Closing Balance at the end of February = xA + xAm/100 - xAn/100

=xA[1+0.01m-0.01n]

= xA^2 ( since 1+0.01m-0.01n =A)

March

Deposit = m% of closing balance of February

= xA^2 m/100

Balance = xA^2 + xA^2m/100

Withdrawal = n% of closing balance of February

= xA^2n/100

Hence Closing Balance at the end of March = xA^2 + xA^2m/100 - xA^2n/100

=xA^2[1+0.01m-0.01n]

= xA^3 ( since 1+0.01m-0.01n =A)

Closing balance of March = Opening balance of January

=> xA^3 = x

=> A^3=1

=> 1+0.01m-0.01n=1

=> 0.01m=0.01n

=> m=n