Question

43. एका रकमेची सरळव्याजाने 5 वर्षांची रास ₹ 24,500 आणि 3 वर्षांची रास
२०₹21,700 आहे, तर द.सा.द.शे. व्याजाचा दर किती?
(1) 8
(2) 9
(3 ) 8.5
(4)7.5​

Answer 1

Given:

एका रकमेची सरळव्याजाने 5 वर्षांची रास ₹ 24,500 आणि 3 वर्षांची रास ₹21,700 आहे

To find:

तर द.सा.द.शे. व्याजाचा दर किती?

Formulas to be used:

$\boxed{\bold{S.I. = \frac{PRT}{100} }}\\\\\boxed{\bold{Amount = P + S.I. }}$

Solution:

As per the question and using the above two formulas, we will form the following equations:

$24500 - P = \frac{PR \times 5}{100}$

$\implies 24500 - P = 0.05PR$

$\implies PR = \frac{24500 - P}{0.05}$

and

$21700 - P = \frac{PR \times 3}{100}$

$\implies 21700 - P = 0.03PR$

$\implies PR = \frac{21700 - P}{0.03}$

∴ $\frac{24500 - P}{0.05} = \frac{21700 - P}{0.03}$

$\implies 735 - 0.03P = 1085 - 0.05P$

$\implies 0.05P - 0.03P = 1085 - 735$

$\implies 0.02P = 350$

$\implies \bold{P = 17500}$

On substituting the value of P in one of the equation, we get

$24500 - 17500 = \frac{17500 \times R \times 5}{100}$

$\implies 7000 = 175 \times R \times 5$

$\implies 7000 = 875 \times R$

$\implies \bold{R = 8\%}$

Thus, the rate of interest is → 8%.

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