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Home / arithmetic / Walid borrowed Tk. 400 for 3 years and Tk. 600 for 5 years and gave a total of Tk. 168 as interest. If the rates of interests are equal for both, what is the rate for interest?

# Walid borrowed Tk. 400 for 3 years and Tk. 600 for 5 years and gave a total of Tk. 168 as interest. If the rates of interests are equal for both, what is the rate for interest?

Solution: Let for the both, rate of interest =Tk. x
So,
Interest on Tk. 100 in 1 year = x%
So, interest on Tk. 100 in 1 year = Tk. x
∴ ”      ‘’          ‘’            1    ‘’ 1 ‘’ = (x÷100)
∴ ”       ‘’         ‘’          400 ‘’ 3 ‘’ = (x×400×3)÷100

= Tk. 12x

Again,

Interest on Tk. 100 in 1 year = Tk. x

∴     ”           ‘’   ‘’       1   ‘’ 1     ‘’ = (x÷100)

∴     ”           ‘’   ‘’   400   ‘’ 3     ‘’ = (x×600×5)÷100

= Tk. 30x

According to the question,

12x + 30x =168

⇒ 42x = 168

⇒ x = 4

∴ The required rate of interest = 4%