Question

the simple interest on a certain sum for 7/2 years at 12% per annum is ₹98 more than the simple interest on the same sum for 5/2 years at 14% per annum . find the sum​

Answer 1

Answer:

$\bigstar\:\boxed{\sf Simple\: Interest=\dfrac{Principal \times Rate \times Time}{100}}$

$\rule{100}{0.8}$

Let the Required Sum for both case be P.

$\underline{\bigstar\:\bf{According\:to\:the\:Question :}}$

$:\implies\sf SI_1-SI_2=Rs.\:98\\\\\\:\implies\sf \dfrac{P \times R_1 \times T_1}{100}-\dfrac{P \times R_2 \times T_2}{100}=Rs.\:98\\\\\\:\implies\sf \dfrac{P \times 12 \times{\large\frac{7}{2}}}{100} - \dfrac{P \times 14 \times{ \large\frac{5}{2}}}{100} = Rs.\:98\\\\\\:\implies\sf \dfrac{P \times 6 \times 7}{100} - \dfrac{P \times 7 \times 5}{100} = Rs.\:98\\\\\\:\implies\sf \dfrac{42P}{100} - \dfrac{35P}{100} = Rs.\:98\\\\\\:\implies\sf \dfrac{7P}{100} = Rs.\:98\\\\\\:\implies\sf P = Rs.\:98 \times \dfrac{100}{7}\\\\\\:\implies\sf P = Rs.\:14 \times 100\\\\\\:\implies\underline{\boxed{\sf P = Rs.\:1400}}$

⠀

$\therefore\:\underline{\textsf{Hence, the required sum will be \textbf{Rs. 1400}}}.$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

We know that,

Simple Interest = Principal × Rate × Time

Now,

According to the Question,

Let P be the sum of interest.

SI₁ - SI₂ = 98

Putting all the values, we get

⇒ P × R₁ × T₁/100 - P × R₂ × T₂/100 = 98

⇒ P × 12 × 7/2/100 - P × 14 × 5/2/100 = 98

⇒ P × 6 × 7/100 - P × 7 × 5/100 = 98

⇒ 42P/100 - 35P/100 = 98

⇒ 42P - 35P/100 = 98

⇒ 7P/100 = 98

⇒ P = 98 × 100/7

⇒ P = Rs. 1400

Hence, the sum of the interest is Rs. 1400.