Question

Simple interst on certain sum at the rate of 10% per annum for 6 years and 7 years differs by Rs 650. What is the sum​

Answer 1

Answer:

The Principal is Rs. 6500.

Step-by-step explanation:

Given :

Rate = 10%

Time = 6 years and 7 years

Simple Interest Differs by = Rs. 650

To find :

The Principal

Solution :

★ $\textsf{\underline{\underline{Case I -}}}$

• Time = 7 years
• Rate = 10
• Principal = y

$\bigstar \: \boxed{\sf{SI = \frac{Principal \times Rate \times Time}{100}}}$

$\sf{\implies} \: SI = \dfrac{y \times 10 \times 7}{100} \\ \\ \sf{\implies} \: SI = \frac{70y}{100}$

Simple Interest for 7 years = $\sf{\dfrac{70y}{100}}$

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Case II -}}}$

• Time = 6 years
• Rate = 10
• Principal = y

$\sf{\implies} \: SI = \dfrac{y \times 6 \times 10}{100} \\ \\ \sf{\implies} \: SI = \dfrac{60y}{100}$

Simple Interest for 6 years = $\sf{\dfrac{60y}{100}}$

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Principal - }}}$

As the Difference between both the simple Interests is Rs. 650, the principal will be =

$\sf{\implies} \: 650 = \dfrac{70y}{100} - \dfrac{60y}{100} \\ \\ \sf{\implies} \: 650 = \frac{10y}{100} \\ \\ \sf{\implies} \: 10y = 650 \times 100 \\ \\ \sf{\implies} \: 10y = 65000 \\ \\ \sf{\implies} \:y = \dfrac{65000}{10} \\ \\ \sf{\implies} \: y = 6500$

Principal = Rs. 6500

$\therefore$ The Principal is Rs. 6500.

Answer 2

Question :

Simple interst on certain sum at the rate of 10% per annum for 6 years and 7 years differs by Rs 650. What is the sum.

Solution :

$\boxed{\purple{Simple\:Interest =\frac{Principal\times Rate\times Time}{100}}}$

$\rule {193}{1}$

In case 1 :

• Rate=10% p.a.
• Time= 7 years
• Principal = Rs x

$\implies Simple\:Interest = \frac{Principal\times Rate\times Time}{100 } \\ \implies Simple\:Interest = \frac{x \times 10 \times 7}{100} \\ \implies Simple\:Interest = \frac{7x}{10}$

$\rule {193}{1}$

In case 2 :

• Rate=10% p.a.
• Time=6 years
• Principal = Rs x

$\implies Simple\:Interest = \frac{Principal\times Rate\times Time}{100 } \\ \implies Simple\:Interest = \frac{x \times 10 \times 6}{100} \\ \implies Simple\:Interest = \frac{6x}{10}$

$\rule {193}{1}$

$\implies \frac{7x}{10} - \frac{6x}{10} = 650 \\ \implies \frac{7x - 6x}{10} = 650 \\ \implies \frac{x}{10} = 650 \\ \implies x = 650 \times 10 \\\implies x = 6500$

$\boxed{\green{\therefore{Hence,\: the\: sum\:is\:Rs\:6500.}}}$