Question

Ramesh deposited a total of Rs. 370000 in three banks. The annual interest rates of the three banks are 4%,5% and 6% respectively. After 1 year, the total amount of interest in three banks is equal. How much money did he deposit in three banks?

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Answer 1

❥${\red{\underline{\underline{\huge{\mathtt{Question:-}}}}}}$

Ramesh deposited a total of Rs. 370000 in three banks. The annual interest rates of the three banks are 4%,5% and 6% respectively. After 1 year, the total amount of interest in three banks is equal. How much money did he deposit in three banks?

❥${\red{\underline{\underline{\huge{\mathtt{Solution:-}}}}}}$

•Ramesh deposited a total of Rs. 370000 in three banks.

• Annual interest of three banks= 4%, 5%,6%.

Consider,

• He deposited in 1st bank = ₹ x.

• He deposited in 2nd bank= ₹ y.

• He deposited in 3rd bank = ₹ z.

★We know that,

${\purple{\boxed{\large{\bold{I=\frac{ptr}{100}}}}}}$

•After 1 year, total interest of 1st bank=$\frac{x×4×1}{100}$=$\frac{4x}{100}$

•After 1 year, total interest of 2nd bank=$\frac{y×5×1}{100}$=$\frac{5y}{100}$

•After 1 year, total interest of 3rd bank=$\frac{z×6×1}{100}$=$\frac{6z}{100}$

According to the question,

x+y+z = 370000..............(i)

$\frac{4x}{100} = \frac{5y}{100} = \frac{6z}{100} ..................(ii)$

Hence,

Consider, 4x=5y=6z= k [ k>0]

.•. x = $\frac{k}{4}$

y = $\frac{k}{5}$

z = $\frac{k}{6}$

• Take (i) no. equation,

x +y+z = 370000

Putting the value of x,y,z:-

→k/4+k/5+k/6 = 370000

→ 37k/60 = 370000

→ k = 600000

Hence,

x = 600000/4

= ${\green{\boxed{\bold{150000}}}}$

y= 600000/5

= ${\green{\boxed{\bold{120000}}}}$

z= 600000/6

= ${\green{\boxed{\bold{100000}}}}$

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Ramesh deposited ₹150000,₹120000 and ₹100000 in three banks respectively.