On what sum of money will the CI for 2 years be the same as the SI on Rs 943 for 10 years the rate of interest being 5 %? In RS?

Q.1.The difference in simple interest and compound interest on a certain sum of money in 2 years at 10 % p.a. is Rs. 50. The sum is

a) Rs. 10000

b) Rs. 6000

c) Rs. 5000

d) Rs. 2000

e) None of these

Sol : Option C
Explanation: If Diff. between SI & CI for 2 years is Rs. x, then Principal = x (100/r)2 P = 50 x (100x100)/(10x10) → P = 5000.

Q.2. The difference in simple interest and compound interest on a certain sum of money in 2 years at 18 % p.a. is Rs. 162. The sum is

a) Rs. 4000

b) Rs. 5200

c) Rs. 4250

d) Rs. 5000

e) None of these

Sol : Option D
Explanation: If Diff. between SI & CI for 2 years is Rs. x, Principal = x (100/r)2 P = 162 x (100x100)/(18x18) → P = 5000.

Q.3. The compound interest on a certain sum of money for 2 years is Rs. 208 and the simple interest for the same time at the same rate is Rs. 200. Find the rate %.

a) 5 %

b) 6 %

c) 7 %

d) 4 %

e) 8 %

Sol : Option E
Explanation: SI = Rs. 200 = Rs. 100 + Rs. 100 CI = Rs. 208 = Rs. 100 + Rs. 108 (In first year SI & CI are equal.)

Therefore, Rs.8 Gap is because of the interest of 1st year interest.

Q.4.The difference between compound interest and simple interest on a certain sum for 2 years at 10 % is Rs. 25. The sum is

a) Rs. 1200

b) Rs. 2500

c) Rs. 750

d) Rs. 1250

e) Rs. 2000

Sol : Option B
Explanation: Apply: Principal = x (100/r)2 where x is the difference in CI & SI for 2 years. ∴ P = 25(100/10)2 = 2500.

Q.5.The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum.

a) 20 %

b) 2.5 %

c) 5 %

d) 15 %

e) 7.5%

Sol : Option A
Explanation: SI for 3 years = 225 → SI for 1 year = 75 ∴ CI for 1 year = 75. So CI for 2nd year = 90 and SI for 2nd year = 75. Difference = 15 ∴ Rate of interest = (15/75)x100 = 20 %

Q.6.The simple interest on a sum of money for 2 years is Rs. 150 and the compound interest on the same sum at same rate for 2 years is Rs. 155. The rate % p.a. is

a) 16 %

b) 20/3 %

c) 12 %

d) 10 %

e) None of these

Sol : Option B
Explanation: SI for 3 years = 150 → SI for 1 years = 75
∴ CI for 1 year = 75. So CI for 2nd year = 80 and SI for 2nd year = 75. Difference = 5 ∴ Rate of interest = (5/75) x 100 = 20/3 %.

Q7.Mihir’s capital is 5/4 times more than Tulsi’s capital. Tulsi invested her capital at 50 % per annum for 3 years (compounded annually). At what rate % p.a. simple interest should Mihir invest his capital so that after 3 years, they both have the same amount of capital?

a) 20/3 %

b) 10 %

c) 50/3 %

d) 1.728 %

e) None of these

Sol : Option C
Explanation: Let, the capital of Tulsi = 4. ∴ Capital of Mihir = 9.

Q8.The difference in simple interest and compound interest on a certain sum of money in 3 years at 10 % p.a. is Rs. 372. The sum is

a) Rs. 8000

b) Rs.9000

c) Rs. 10000

d) Rs. 12000

e) None of these

Sol : Option D
Explanation: Let us assume P= Rs. 1000. SI= Rs. 300, CI = Rs. 331 Difference = 331 - 300 = Rs. 31. Applying the unitary method, the difference Rs. 372 is 12 times Rs. 31.

Therefore, the principle will also be 12 times of Rs. 1000 i.e. Rs. 12000.

Q9.Sahil’s capital is 1/6 times more than Chaya’s capital. Chaya invested her capital at 20 % per annum for 2 years (compounded annually). At what rate % p.a. simple interest should Sahil invest his capital so that after 2 years, they both have the same amount of capital?

a) 10%

b) 11 5/7%

c) 20%

d) 13 5/7%

e) None of these

Sol : Option B
Explanation: Let, the capital of Sahil = 6. ∴ Capital of Chaya = 7

Q10.The difference in simple interest and compound interest on a certain sum of money in 3 years at 20 % p.a. is Rs. 640. The sum is

a) Rs. 5000

b) Rs. 8500

c) Rs. 8250

d) Rs. 6000

e) None of these

Sol : Option A
Explanation: Let us assume P= Rs. 1000, SI = Rs. 600, CI = Rs. 728 Difference= 728 – 600 = Rs. 128 Applying the unitary method, the difference Rs. 640 is 5 times Rs. 128.

Therefore, the principle will also be 5 times of Rs. 1000 i.e. Rs. 5000.

P = Rs. 9430R = 5%

T = 10 years

SI = `[ 9430 xx 5 xx 10 ]/100` = Rs. 4715

Let sum = X
CI = 4715, T = 2 years, Rs= 5%

CI = AP

`4715 = "X"[ 1 + "R"/100 ]^"T" - "X"`

`4715 = "X"[ 1 + 5/100 ]^2 - "X"`

`4715 = "X"|(21/20)^2 - 1|`

`4715 = "X"([ 441 - 400]/400)`

`"X" = [ 4715 xx 400]/41` = Rs. 46,000

Thus principal from = Rs. 46,000