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Question
A person has Rs30000 to invest.He wants to invest some amount in the fixed deposit and remaining in saving account.The interest rates are 7 % and 5 % p.a. for the fixed deposit and the saving account respectively.Find how he should divide the total amount Rs30000 in two accounts if he wants to get the annual interest as
1.Rs1800
2.Rs2000

Answer
Jay,
Here is the answer and approach to your question:

Let us assume that the person invests Rs x in fixed deposit and Rs y in savings account. Since he has total Rs 30,000, we get

x + y = 30,000 -------------------- (1)

The formula for interest (I) is,

I = (P*T*R)/100 --------------------- (2)
where,
I = Interest
P = Principal
T = Time duration of the deposit in years
R = Interest rate p.a


Let us denote interest earned on fixed deposit by If and interest earned on savings account by Is.

For fixed deposit, I = 7% and T = 1 year, P = x
Thus, interest earned on fixed deposit (If) = x*1*7/100 = 7x/100
If = 7x/100 --------------------------- (3)

For savings account, I = 5% and T = 1 year, P = y
Thus, interest earned on savings account (Is) = y*1*5/100 = 5y/100
Is = 5y/100 --------------------------- (4)

Thus total interest earned (It) = If + Is
Putting values from equation (3) and (4), we get
It = 7x/100 + 5y/100
It = (7x+5y)/100 ---------------------------------- (5)

But, from (1) we get,
x = 30,000 - y -------------------- (6)

Putting this in equation (5), we get,

It = (7(30000-y)+ 5y)/100
It = (210000-7y+5y) /100
It = (210000-2y)/100 ----------------(7)

Now let us solve for case 1.
Total interest is Rs 1800.
It = 1800
Putting this in equation (7) above, we get
1800 = (210000-2y)/100
180000 = 210000-2y
2y = 30000
y = 15000 ---------------- (8)
From (6), we get,
x = 30,000 - 15,000 = 15,000 ----------(9)

Thus, to get total interest of Rs 1800, the person should invest Rs 15,000(x) in fixed deposit and Rs 15,000 (y) in savings account.

For the second case of total interest = Rs 2000, I encourage you to solve it using above method on your own. Please let me know if you face any problem. The answers are x = Rs 25,000 and Y = 5,000; you can verify your answer with this answer.

All the best

Regards,
Pawan

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Pawan Musale

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I can answer questions wrapped in words. This includes questions related to Logic, Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc.

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Tutoring on www.allexperts.com since long time.

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I am Bachelor of Engineering from the reputed institute in India.

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