Question

Rahul deposit a sum of rupees 15000 in a bank for 3 years he also in West thousand for the same period but at the rate of 5% higher than the first he got a total interest of rupees 5910 from both his deposit at the end of 3 years find the rate of interest find the rate of simple interest on the on rupees 15000 and rupees 1000

Answer 1

Given :-

• Deposit Rs.15000 for 3 years.
• Deposit Rs.1000 For 3 years at 5% higher Rate.
• Total interest on both = Rs.5910 .

To Find :-

• Rate of interest on Both sum ?

Solution :-

we know That, SI is given by (P*R*T)/100 .

Let Rate on which Rs.15000 is deposit is R% per annum.

Than Rate on which Rs.1000 is Deposit is is (R+5)% per annum.

So,

→ [ (15000*R*3)/100 ] + [ (1000*(R+5)*3)/100 ] = 5910

→ [ 150*3R ] + [ 10 * (3R + 15) ] = 5910

→ 450R + 30R + 150 = 5910

→ 480R = 5910 - 150

→ 480R = 5760

→ R = 12% .

Hence,

→ Rs.15000 is Deposit at a rate of = 12% Per Annum.

→ Rs.1000 is Deposit at a Rate of = (R + 5) = (12+5) = 17% per Annum.

Answer 2

Answer:

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

$\frak{first}\begin{cases}\textsf{Principal = Rs. 15,000}\\\textsf{Rate = r\% p.a.}\\\textsf{Time = 3 years}\end{cases}$

$\frak{second}\begin{cases}\textsf{Principal = Rs. 1,000}\\\textsf{Rate = (r + 5)\% p.a.}\\\textsf{Time = 3 years}\end{cases}$

$\rule{160}{1}$

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

$:\implies\tt SI_1+SI_2=Total\: Interest\\\\\\:\implies\tt \dfrac{(P_1 \times R_2 \times T)}{100}+\dfrac{(P_2 \times R_2 \times T)}{100}=5910\\\\\\:\implies\tt \dfrac{15000 \times r \times 3}{100} + \dfrac{1000 \times (r + 5) \times 3}{100} = 5910\\\\\\:\implies\tt \dfrac{3}{100} \bigg((15000 \times r) + (1000 \times (r + 5)) \bigg) = 5910\\\\\\:\implies\tt 15000r + 1000r + 5000 =5910 \times \dfrac{100}{3}\\\\\\:\implies\tt 16000r + 5000 =197000\\\\\\:\implies\tt 16000r =197000 - 5000\\\\\\:\implies\tt 16000r =192000\\\\\\:\implies\tt r = \dfrac{192000}{16000}\\\\\\:\implies\tt r =12\%$

⠀

$\bullet\:\:\textsf{First Deposit [Rs. 15,000] = r = \textbf{12 \%}}\\\bullet\:\:\textsf{Second Deposit [Rs. 1000] = (r + 5) = \textbf{17\%}}$