SSC CGL 20201)The simple interest on a sum of money for 3 years at an interest rate of 6% p.a is Rs. 6750. What will be the CI on the same sum at the same rate for same period, compounded annually:

Correct Option: D

Rs.7163

SI = PRT/100 (put R=6, SI = 6750 and T=3 and calculate P)

P = 37500

Diff b/w CI and SI for 3 years = C.I - S.I = P(R/100)²(R/100 + 3)

C.I = Rs 7163 (aprox)

SSC CGL 20192)A sum of Rs.18000 is lent at 10% p.a. compound interest, compounded annually. What is the difference between the compound interest for 3rd year and 4th year ?

Correct Option: B

Rs. 217.80

Compound interest = \(p(1 + \frac{r}{100})^t - p;\)

Amount at the end of 2 years = \(18000 (1+10/100)^2 = 18000 (1.1)^2 = Rs 21780;\)

Amount at the end of 3 years =\( 18000 (1+10/100)3\)= Rs 23958;

Interest for 3rd year = Amount at end of 3rd year - Amount at end of 2nd year = 23958 - 21780 = Rs 2178;

Amount at the end of 4 years = \(18000(1+10/100)^4\) = Rs 26353.8;

Interest for 4th year = Amount at end of 4th year - Amount at end of 3rd year = 26353.8 - 23958 = Rs 2395.8;

Difference between interest of 3rd year and of 4th year = 2395.8 - 2178 = Rs 217.8

SSC CGL 20193)A sum of Rs. 8,400 amounts to Rs. 11,046 at 8.75% per annum simple interest in certain time. What is the simple interest on the sum of Rs. 9,600 at the same rate for the same time ?

Correct Option: D

Rs. 3,024

Simple interest = \(\frac{prt}{100};\)

A sum of ₹8,400 amounts to ₹11,046 at 8.75% p.a.

So, interest = 11046 - 8400 = 2646;

2646 =\( \frac{8400 \times 8.75 \times t}{100};\)

t = 2646/735 = 3.6 years;

Interest when principle Rs. 9600 =\( \frac{9600 \times 8.75 \times 3.6}{100}\) = Rs.3024

SSC CGL 20194)What will be the compound interest on a sum of ₹31,250 for 2 years at 12% p.a., if the interest is compounded 8-monthly?

Correct Option: B

Rs. 8,116

Interest is compounded 8-monthly so,

Time = \(2 \times 3/2\) = 3 years

Rate = \(\frac{12}{3/2} \)= 8%

P = 31250

Compound interest =\( p(1 + \frac{r}{100})^t - p
= 31250(1 + \frac{8}{100})^3 - 31250
= 31250 \times \frac{108}{100} \times \frac{108}{100} \times \frac{108}{100}\) - 31250 = 39366 - 31250 = Rs.8116

SSC CGL 20195)A sum of ₹5,000 is divided into two parts such that the simple interest on the first part for \(4\frac{1}{5} \)years at \(6\frac{2} {3}\% p.a \). is double the simple interest on the second part for \( 2\frac{3}{4} \) years at 4% p.a. What is the difference between the two parts?

Correct Option: B

Rs. 600

Interest on 1st part = (r \times t)%;

\(4\frac{1}{5} \times 6\frac{2}{3}\)% =\( \frac{221}{5} \times \frac{20}{3}%\)

= 28%;

Interest on 2nd part,

\(2\frac{3}{4} \times 4% = \frac{11}{4} \times 4%\)

= 11%;

Let the principle of 1st and 2nd part be p and q respectively.

ATQ,

28%p =\( 2\times 11%q;\)q;

14p = 11q;

p : q = 11 : 14;

(11 + 14 = 25) units = 5000;

Difference between the two parts = 14 - 11 = 3 units;

3 units = \(\frac{5000}{25} \times 3\) = Rs.600;

So, difference between the two parts is Rs.600.

SSC CGL 20196)A person invested one-fourth of the sum of ₹25,000 at a certain rate of simple interest and the rest at 4% p.a. higher rate. If the total interest received for 2 years is ₹4,125, whatis the rate at which the second sum was invested?

Correct Option: B

9.25%

SSC CGL 20197)A certain loan was returned in two equal half-yearly installments each of ₹6,760. If the interest rate was 8% p.a., compounded annually, how much was the interest paid on the loan?

Correct Option: D

₹ 770

Installments in case of compound interest is

P = x/(1 + r/100) + x/(1 + r/100)^{2} ....x/(1 + r/100)^{n}

Since the loan is paid half yearly, thus we will use the formula by adjusting the que like rate of interest to half r = 4% and taking time duration n = 2., Given, (each installment) x = 6,760

⇒ P = [6,760/(1 + 4/100)] + [6,760/(1 + 4/100)^{2}]

⇒ P = 6500 + 6250 = 12750

Total Rs paid = 6760 × 2 = 13520

Interest paid = 13520 – 12750 = 770

SSC CGL 20198)A certain sum amounts to ₹4,205.55 at 15% per annum in \(2\frac{2}{5}\) years, interest is compounded yearly. The sum is:

Correct Option: D

₹ 3,000

\(A=P(1 + \frac{R}{100})^t \)

R = 15% for the initial 2 years, then the time period remaining is 2/5 years, hence, if we increase time to 1 year, then the rate will be \(\frac{2}{5} \times15 = 6\)%

\(4205.55 = P(1 + \frac{15}{100})^2(1 + \frac{6}{100}) \)

P = Rs 3000

SSC CGL 20199)A sum of ₹10,500 amounts to ₹13,825 in \(3\frac{4}{5}\) years at a certain rate per cent per annum simple interest. What will be the simple interest on the same sum for 5 years at double the earlier rate?

Correct Option: B

₹ 8,750

SSC CGL 201910)A sum lent out at simple interest amounts to ₹6076 in 1 year and ₹7504 in 4 years. The sum and the rate of interest p.a. are respectively:

Correct Option: B

₹5,600 and 8.5%

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