 Simple Interest set 1  final amount initial principal balance annual interest rate time (in years)

1] From a bank, Ram and Shyam together took a certain amount under SI
and they lent the total amount to Mohan at 2% more SI. 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?
A. Rs. 10000
B. Rs. 20000
C. Rs. 5000
D. Rs. 25000
E. Can’t be determined

 Let Ram took Rs. a and Shyam took Rs. bLet the rate of interest was r% per annumThey lent Rs. (a + b) to Mohan at the rate of (r + 2)% per annumFor Ram,The total interest received on Rs. a = a × 4 × (r + 2)/100The total interest paid by Ram to the bank = a × r × 4/100The total interest earned by Ram after paying the interest to the bank= a × 4 × (r + 2)/100 – a × r × 4/100 = 8a/100 —— (i)For Shyam,The total interest received on Rs. b = b × 4 × (r+ 2)/100The total interest paid by Shyam to the bank = b × r × 4/100The total interest earned by Ram after paying the interest to the bank= b × 4 × (r + 2)/100 – b × r × 4/100 = 8b/100 —— (ii)From the question,8a/100 – 8b/100 = 400a – b = 50 × 100 = Rs. 5000Hence, option C is correct.

2] 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.
A. Rs. 34000
B. Rs. 19000
C. Rs. 35000
D. Rs. 14000
E. Rs. 30000

 Let the total investment in scheme B be Rs.x, then(49000 – X) × 5/100 + X × 12/100 = 4900X = 5/7 × 49000 = Rs. 35000Hence, option C is correct.

3] After four years, the SI obtained on Rs. 8250 at the rate of (x + 4)% is Rs. 1320 more than the SI obtained at the rate of 8% per annum. Find the
value of ‘x’.

A. 12%
B. 10%
C. 8%
D. 15%
E. None of these

 According to the question,8250 × (x + 4) % × 4 – 8250 × 8% × 4 = 1320330 (x + 4) – 2640 = 1320330 (x + 4) = 3960x + 4 = 12 ; x = 8So, the value of x = 8%Hence, option C is correct.

4] 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 SI 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?
A. Rs. 18000
B. Rs. 9400
C. Rs. 9000
D. Rs. 15000
E. None of these

 Ratio of profit = 2000 : 900 = 20 : 9Let amount invested by Raghav be KRatio of investment = 12 × 7200 : 6 × K = 14400 : K = 20 : 9K = Rs 6480Let original Salary of Raghav = R60 %( R) at 40% p.a for 6 months60 × R × 40 × 1 = 6480 – 0.6R100 200R = Rs. 9000Hence, option C is correct.

5] A sum of Rs. 12,000 invested at 8% SI becomes Rs. 15840 in x years and
another sum of Rs. 15,000 invested at 12% SI becomes Rs. 18,600 in y
years. Find the value of x + y.

A. 6
B. 7
C. 5
D. 8
E. 10

 1st Case :Interest = A – P = 3840Now, I = P × R × N1003840 = (12000 × 8 × x)/100x = 42nd Case :Interest = 18600 – 15000 = 36003600 = (15000 × 12 × y)/100y = 2x + y = 4 + 2 = 6Hence, option A is correct.

 NOTE: SI stands for Simple Interest

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