Maths - Simple Interest Questions with Explanation!

The salary of a man is Rs. 60000, from which he deposits x% amount at 13% simple interest. If the accumulated amount for the sum deposited after 3 years was Rs. 29190, then find the value of ‘x’. 

According to the question,

(x% of 60000) +	(x% of 60000) × 13 × 3	= 29190
	100

600x + 234x = 29190

834x = 29190 ; x = 35

So, the value of ‘x’ = 35

Rayan invested a total of Rs.49000 in two different schemes A and B. The scheme A which offers interest at a rate of 5% per annum and scheme B offers interest at a rate of 12%. If the total interest earned by Rayan after 1 year is Rs.4900 then find the sum invested in scheme B.

Let the total investment in scheme B be Rs.x, then

(49000 – X) ×	5	+ X ×	12	= 4900
	100		100

X =

5

× 49000 = Rs. 35000

Deepika deposited Rs. 1000 in a fund in 2019 which provides simple interest. The interest rate on the fund increases by  3% every year. If the interest rate at the time of amount deposit was 10%, find the interest earned by her after 9 years. 

Amount deposited = Rs. 1000

Interest earned by him after 9 years

=	{1000 × (10 + 13 + 16 + 19 +.... upto 9 terms)}
	100

→ Here we can use the formula of Arithmetic Progression,

n	{2a + (n – 1) d}
2

→ 10 ×	[	9	{2 × 10 + (9 – 1) × 3}	]
		2

→ 45 × 44 = 1980

→ Interest earned = Rs. 1980

Aman and Raghav are two friends. Aman started a business with an investment of Rs 7200, while Raghav puts 60% of his salary at 40% p.a simple interest for 6 months; Raghav takes the amount received after 6 months and joins Aman in the business. If Aman receives a profit of Rs. 2000 out of a total profit of Rs. 2900 at the end of 1 year, what was the original salary of Raghav?

Ratio of profit = 2000 : 900 = 20 : 9

Let amount invested by Raghav be K

Ratio of investment = 12 × 7200 : 6 × K = 

14400 : K = 20 : 9

K = Rs 6480

Let original Salary of Raghav = R

60 %( R) at 40% p.a for 6 months

60	× R ×	40	× 1 = 6480 – 0.6R
100		200

R = Rs. 9000

From a bank, Ram and Shyam together took a certain amount under simple interest and they lent the total amount to Mohan at 2% more simple interest. At the end of 4 years, the total money earned by Ram after paying the interest to the bank was Rs. 400 more than that of Shyam. From the bank, the total amount taken by Ram was how much more than that of Shyam?

Let Ram took Rs. a and Shyam took Rs. b

Let the rate of interest was r% per annum

They lent Rs. (a + b) to Mohan at the rate of (r + 2)% per annum

For Ram,

The total interest received on Rs. a = a × 4 ×	r + 2
	100

The total interest paid by Ram to the bank = a × r ×	4
	100

The total interest earned by Ram after paying the interest to the bank

= a × 4 ×	r + 2	– a × r ×	4	=	8a	------ (i)
	100		100		100

For Shyam,

The total interest received on Rs. b = b × 4 ×	r+ 2
	100

The total interest paid by Shyam to the bank = b × r ×	4
	100

The total interest earned by Ram after paying the interest to the bank

= b × 4 ×	r + 2	– b × r ×	4	=	8b	------ (ii)
	100		100		100

From the question,

8a	–	8b	= 400
100		100

a – b = 50 × 100 = Rs. 5000

Arnab deposited Rs. 14500 in SBI mutual fund which offers simple interest at the rate of 9%. The simple interest obtained from SBI is deposited in Birla Sun Life mutual fund at the rate of 12% simple interest. If the time period for depositing in SBI and Birla were 2 years and 5 years respectively, then find the total simple interest earned by Arnab. 

Simple interest earned from SBI mutual fund

=	14500 × 9 × 2	= Rs. 2610
	100

Simple interest earned from Birla Sun Life mutual fund

=	2610 × 12 × 5	= Rs. 1566
	100

Total simple interest earned = 2610 + 1566 = Rs. 4176

The rate of interest for the first 2 years is 3% per annum, for the next 3 years is 8% per annum, and for the period beyond 5 years is 10% per annum. If the man withdraws total amount of Rs. 5320 after 6 years, find the sum he deposited?

Let principal be Rs P.

S.I. = S.I for 1 & 2 year + S.I. for 3,4&5 year +S.I. for 6th year

S.I. =	P × R1 × T1	+	P × R2 × T2	+	P × R3 × T3
	100		100		100

⇒ P +  P	(	2 × 3 + 3 × 8 + 1 × 10	)	= 5320
		100

⇒ P = Rs. 3800

Alternate:

S.I. for six years = 40%

140% of P =5320

P = 3800

Andy lends a sum of money at R% simple interest for R years such that sum received by him is 9/16 times more of what he lends. Find the value of R.

Let the sum be Rs x

S.I =	(	9	)	x
		16

Let rate be R% and time = R years

S.I =	(	PRT	)
		100

(x × R × R)	=	(	9	)	x ⇒ R2 =	900	⇒ R =	30
100			16			16		4

R = 7.5 

Sanjay borrowed certain amount of money at simple interest at the rate of 5% p.a. for the first three years, 10% p.a. for the next five years and 12% p.a. for the period beyond 8 years. If the total interest paid by him at the end of 12 years is Rs. 6780, how much money did he borrow?   

5% for first three years,

 

3 × 5% = 15%

 

10% for next five years,

 

5 × 10% = 50%

 

Time = 12 years,

 

12% for the next 4 years,

 

4 × 12% = 48%

 

Total rate interest = (15 + 50 + 48)% = 113%

 

113% corresponds to 6780

 

1% corresponds to 6780/113 = 60

 

100% will correspond to 6000.

 

Principal = Rs. 6000  

A certain sum 10M Invested at simple Interest becomes 130M in 30 years. If the same amount invested with same rate of Interest but at Compound Interest, it will become ___ after two years? 

As Amount becomes 130M, so Interest is 130M - 10M = 120M

Interest earned is 120M in 30 years.

I =	PRN
	100

120M =	(10M × R × 30)
	100

R = 40 %

Now, the same amount is Invested at Compound Interest.

Amount = Principal ×	(	1 +	Rate of Interest	)	Time Period
			100

= 10M × (1 + 0.4)2

= 10M × 1.96

= 19.6M

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