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Simple interest
1.
Black Holes of
Aptitude-Simple Interest ©Mayank Gupt-makguffaw@gmail.com,9990123477 Simple Interest Interest: (I) Interest is money paid to the lender by the borrower for using his money for a specified period of time. Various terms and their general representation are as follows: Principal(P): The original sum borrowed Time (t): Time for which money is borrowed. Rate of Interest(r): Rate at which interest is calculated on the original sum. Amount (A): Sum of Principal and Interest. (P+I). Simple Interest (SI): When interest is calculated every year (or every time period) on the original Principal, such interest is called Simple Interest. SI = P × r × t 100 A=P+I A=P+𝑡 × 𝑥 Type I: Exp 1: A Sum of Rs. 1600 gives a SI of Rs. 252 in 2 years and 3 months. The rate of interest is: Solution: P=1600 SI=252 t= 2 years 3 months=2+ 3 12 = 9 4 r=? SI = P × r × t 100 252 = 1600 × r × 9 100 × 4 =7%
2.
Black Holes of
Aptitude-Simple Interest ©Mayank Gupt-makguffaw@gmail.com,9990123477 Type II: Times Part A: Simple Interest becomes x times of Principal Take P=1 SI=x Exp2: In what time will the SI be 2 5 of the principal at 8 ppa. Solution: SI = P × r × t 100 2 5 = 1 × 8 × t 100 t=5 years Part B: A sum of money becomes x times of itself. Take P=1 SI=x-1 Exp3: A sum of money becomes 7 6 times of itself in 3 years at a certain rate of SI .The rate ppa (percent per annum) is: Solution: P=1 SI= 7 6 -1 = 1 6 SI = P × r × t 100 1 6 = 1 × r × 3 100 r=5 5 9 %
3.
Black Holes of
Aptitude-Simple Interest ©Mayank Gupt-makguffaw@gmail.com,9990123477 Part C: A sum of money becomes x times of Amount. A=P+I 1=P+x×1 P=1-x Take SI=x P=1-x Exp 4: At what rate ppa will the SI on a sum of money be 2 5 of the amount in 10 years. Solution: SI= 2 5 P=1- 2 5 = 3 5 SI = P × r × t 100 2 5 = 3 5 × r × 10 100 r=6 2 3 % Part D: x times in t1 years y times in t2 years 𝑥 − 1 𝑦 − 1 = t1 t2 Exp 5: A certain sum of money becomes 3 times of itself in 20 years at SI. In How many years does it become double of itself at SI? Solution: 𝑥 − 1 𝑦 − 1 = t1 t2
4.
Black Holes of
Aptitude-Simple Interest ©Mayank Gupt-makguffaw@gmail.com,9990123477 3 − 1 2 − 1 = 20 t2 t2 = 10 years Type III Part A: A sum of money P amounts to A1 in t years, it will amount to A2 if it was put at r % higher. A2= A1+ P×r×t 100 Exp 6: A sum of 800 amounts to 920 in 3 years at SI. If the rate is increased by 3ppa .What will be the sum amount to in the same period. A2= 920+ 800×3×3 100 =992 Part B: A sum was put at SI at a certain rate for t years .Had it been put at r ppa higher, it would have fetched D Rs. more find the sum: P= D×100 𝑡×𝑟 Exp 7: A sum of money was lent at SI at certain rate for 3 years .Had it been lent at 2.5 % higher rate, it would have fetched 540 more. The money lent was: P= D×100 𝑡×𝑟 P= 540×100 3×2.5 =7200 Type IV: The SI on certain sum of money at r1 ppa for t1 years is Rs. D more than the interest on the same sum for t2 years at r2 ppa. P = D×100 (r1×t1−r2×t2)
5.
Black Holes of
Aptitude-Simple Interest ©Mayank Gupt-makguffaw@gmail.com,9990123477 Type V: Annual Payment Annual Payment= P×100 𝑛×100+ 𝑛(𝑛−1)×𝑟 2 Exp 8: What annual payment will discharge a debt of Rs. 848 in 4 years at 4ppa. Annual Payment= P×100 𝑛×100+ 𝑛(𝑛−1)×𝑟 2 Annual Payment= 848×100 4×100+ 4(4−1)×4 2 =200 Type VI: If certain money amounts to A1 in t1 years, A2 in t2 years. Find Principal and rate of interest: Solution: A1= P+ t1× x…………………(i) A2= P+ t2× x………………..(ii) (ii)-(i) X= A2−A1 t2−t1 ……………………(iii) ( iii) in (i) P = A1t2−A2t1 t2−t1 From SI = P × r × t 100 R = 100×(A2−A1) (A1t2−A2t1) Exp 9: A certain sum of money amounts to 756 in 2 years and 873 in 3.5 yeas at a certain rate find P and SI:
6.
Black Holes of
Aptitude-Simple Interest ©Mayank Gupt-makguffaw@gmail.com,9990123477 Solution: 756=P+2×x……..(i) 873=P+3.5×x………(ii) X=78…………(iii) (iii)in (i) or (ii) P=600 from SI = P × r × t 100 R=13% Type VII Partly at x % partly at y %,avg. is r % Ratio of principal= (𝑦−𝑟) (𝑟−𝑥) Exp10: A sum of Rs. 10000 lent partly at 8 % and remaining at 10ppa.If the yearly interest on avg. is 9.2%, the two parts are: Solution: Ratio of principal= (𝑦−𝑟) (𝑟−𝑥) Ratio of principal= (10−9.2) (9.2−8) =2:3 Parts will be 4000 and 6000
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