Question

1. A man invested ₹3500, part of it in a yearly interest rate of 4% and the

rest at 5%. He receives a total annual interest of ₹153. How much did he

invest at each rate? [Answer: ₹2200 at 4% and ₹1300 at 5%]​

Answer 1

Solution :

$\bf{\small{\red{\underline{\bf{Given\::}}}}}$

A man invested Rs.3500, part of it in a yearly interest rate of 4% and the rest at 5%. He receives a total annual interest of Rs.153.

$\bf{\small{\red{\underline{\bf{To\:find\::}}}}}$

He invest at each rate.

$\bf{\small{\red{\underline{\bf{Explanation\::}}}}}$

Let the man invest in a yearly interest rate 4% p.a = Rs. r

Let the man invest in a yearly interest rate 5% p.a = Rs.(3500-r)

We know that formula of the Simple Interest :

$\boxed{\sf{Simple\:Interest\:(S.I.)=\frac{P\times R\times T}{100} }}}}$

$\bullet\:{\sf{Principal\:(P)_{1}=Rs.r}}\\\\ \bullet{\sf{Rate\:(R)_{1}=4\%}}\\\\\bullet{\sf{Time\:(T)_{1}=1\:years}}$

&

$\bullet\:{\sf{Principal\:(P)_{2}=Rs.(3500-r)}}\\\\ \bullet{\sf{Rate\:(R)_{2}=5\%}}\\\\\bullet{\sf{Time\:(T)_{2}=1\:years}}$

A/q

$\longrightarrow\sf{\dfrac{r\times 4\times 1}{100} +\dfrac{(3500-r)\times 5\times 1}{100}=153} \\\\\\\longrightarrow\sf{\dfrac{r\times 4}{100} +\dfrac{(3500-r)\times 5}{100} =153}\\\\\\\longrightarrow\sf{\dfrac{4r}{100} +\dfrac{17500-5r}{100} =153}\\\\\\\longrightarrow\sf{\dfrac{4r}{100} +\dfrac{175\cancel{00}}{\cancel{100}} -\dfrac{5r}{100} =153}\\\\\\\longrightarrow\sf{\dfrac{4r}{100} -\dfrac{5r}{100} +175=153}\\\\\\\longrightarrow\sf{\dfrac{4r-5r}{100} +175=153}$

$\longrightarrow\sf{\dfrac{-r}{100} +175=153}\\\\\\\longrightarrow\sf{\dfrac{-r}{100} =153-175}\\\\\\\longrightarrow\sf{\dfrac{-r}{100} =-22}\\\\\\\longrightarrow\sf{-r=-22\times 100}\\\\\\\longrightarrow\sf{\cancel{-}r=\cancel{-}2200}\\\\\\\longrightarrow\sf{\red{r=2200}}$

Thus;

The man invest in a yearly interest rate 4% p.a = Rs.2200.

The man invest in a yearly interest rate 5% p.a = Rs.(3500-2200)

The man invest in a yearly interest rate 5% p.a = Rs.1300.

Answer 2

Given:

A man invested ₹3500, part of it in a yearly interest rate of 4% and the rest at 5%. He receives a total annual interest of ₹153.

To find:

He invest at each rate.

Explanation:

Let the man invest in a yearly interest rate 4% p.a = Rs r

Let the man invest in a yearly interest rate 5% p.a = Rs (3500 - r)

We know that formula of the simple interest:

simple interest (S.I.) = p × r × t /100

• principal (p) = Rs. r

• Rate (r) = 4%

• Time (t) = 1 year

&

• principal (p) = Rs. (3500 - r)

• Rate (r) = 5%

• Time (t) = 1 year

A.T.Q

r × 4 × 1 /100 = (3500 - r) × 5 × 1 / 100 = 153

r × 4 / 100 = (3500 - r) × 5 × 1 / 100 = 153

4r/100 + 17500 - 5r /100 = 153

4r/100 - 5r/100 + 175 = 153

-r/100 = 153 - 175

-r/100 = -22

-r = -22 × 100

r = 2000

Thus,

The man invest in a yearly interest rate 4% p.a = Rs 2200

The man invest in a yearly interest rate 5% p.a = Rs (3500 - 2200)

= Rs 1300

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