Question

A sum of money invested at compound
interest amounts to * 9,248 in 2 years 3
and to 9,826 in 3 years. The sum of
money is
(1) 8,192
(2)
8,526
(3) 8,670
(4) 8,720​

Answer 1

Gɪᴠᴇɴ :-

• Sum of Money Amounts to Rs.9248 after 2 Years..
• Sum of Money Amounts to Rs.9826 after 3 Years..

Tᴏ Fɪɴᴅ :-

• The sum of money is ?

Sᴏʟᴜᴛɪᴏɴ :-

it has been given that, the amounts becomes Rs.9248 after 2 Years & Rs.9826 after 3 Years..

So, we can conclude That, at some Rate Money was increased in 1 Year From Previous Year amount .

→ Increased Sum From 2nd year to 3rd Year = 9826 - 9248 = Rs.578 .

→ Money Increased From = Rs.9248 .

Therefore,

→ Required Rate % = (578 * 100) / 9248 = 6(1/4) = (25/4)% .

______________

Now,

→ Amount After 2 Years = Rs.9248

→ Rate = (25/4)%

→ Let Principal = P .

So,

→ Amount = Principal *[ 1 + (Rate/100)]^Time

→ 9248 = P * [ 1 + (25/4)/100 ]²

→ 9248 = P * [ 1 + 1/16 ]²

→ 9248 = P * (17/16)²

→ 9248 = P * (289/256)

→ P = (9248 * 256) / 289

→ P = ₹ 8192. (Option 1.) (Ans.)

Hence, The Sum of Money is ₹ 8192 .

Answer 2

Answer:

When we will Subtract Amount of Concecutive Years, we will Get Interest of 1 year and that is both CI & SI.

$\underline{\bigstar\:\textbf{Simple Interest of 1 year will be :}}$

$:\implies\sf SI=Amount_{(Year\:3)}-Amount_{(Year\:2)}\\\\\\:\implies\sf \dfrac{Principal \times Rate \times Time}{100}=9826-9248\\\\\\:\implies\sf \dfrac{9248 \times Rate \times 1}{100}=578\\\\\\:\implies\sf Rate=\dfrac{578 \times 100}{9248}\\\\\\:\implies\sf Rate=\dfrac{25}{4}\%\\\\\\:\implies\sf Rate=\dfrac{1}{16}$

$\rule{150}{1}$

$\underline{\bigstar\:\textbf{Amount compounded for 2 years :}}$

$:\implies\sf Amount = P \times \bigg(1 +\dfrac{r}{100}\bigg)^{t}\\\\\\:\implies\sf 9248 = P \times \bigg(1 +\dfrac{1}{16}\bigg)^{2}\\\\\\:\implies\sf 9248 = P \times \bigg(\dfrac{17}{16}\bigg)^{2}\\\\\\:\implies\sf 9248 \times \dfrac{16}{17} \times \dfrac{16}{17}=P\\\\\\:\implies\underline{\boxed{\sf Principal=Rs.\:8192}}$

⠀

$\therefore\:\underline{\textsf{Hence, The sum of money is 1) \textbf{Rs. 8,192}}}.$