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b) Madan Bahadur deposited a sum of money at his bank account at the rate of 10% p.a.. After 5 years, he received Rs 1900, the net interest when 5% of the total interest was charged as income tax. Find, how much sum was deposited by him?​

Sagot :

According to the total interest gained, the sum deposited by Madan Bahadur was Rs 4,000.

What is the formula for total interest?

For the principal [tex]P[/tex] and the rate of interest [tex]r\%[/tex] per annum, the total interest after [tex]t[/tex] years is given by the formula: [tex]I=\dfrac{Prt}{100}[/tex].

Given that after 5 years Madan Bahadur got a net interest of Rs 1900 after charging 5% of the total interest as income tax where the rate of interest was 10% p.a.

Suppose the sum deposited was [tex]P[/tex] and the total interest was [tex]I[/tex].

So, the net interest would be [tex]I_n=I-I\times \frac{5}{100}=\frac{19I}{20}[/tex].

Now, given that the net interest [tex]I_n=1900[/tex]. So, we must have [tex]\frac{19I}{20}=1900\\\Longrightarrow I=\frac{1900\times 20}{19}\\\therefore I=2000[/tex]    (1)

Thus, the total interest after 5 years is Rs 2,000.

Also, using the above formula for the total interest, the total interest of the sum [tex]P[/tex] at the rate [tex]r=10\%[/tex] p.a. after [tex]t=5[/tex] years would be [tex]I=\frac{Prt}{100}=\frac{P\times 10\times 5}{100}=\frac{P}{2}[/tex].

So, we must have from (1),

[tex]\frac{P}{2}=2000\\\Longrightarrow P=2000\times 2\\\therefore P=4000[/tex]

Therefore, according to the total interest gained, the sum deposited by Madan Bahadur was Rs 4,000.

To know more about total interest, refer: https://brainly.com/question/13005100

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