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:
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 20202)A certain sum amounts to Rs.280900 in 2 years at 6% per annum, interest compounded annually. The sum is:
Rs.250000
Sum = p; Time(t) = 2 years; r = 6%; Amount = 280900; \(Amount={P(1+\frac{r} {100})^t} \);
\(280900=P(1+\frac{6}{100})^2\) = Rs. 250000
SSC CGL 20203)The compound interest on a certain sum at the end of two years is Rs.408. The simple interest on the same sum for the same time is Rs.400. The rate of interest per annum is:
4%
S.I. for 2 years = Rs. 400; so S.I. for 1 year =\({400\over2 }= 200\); \({P\times r\times t\over100}=200\); ⇒ Pr = Rs. 20000; According to the question, \({(P+200)\times r\times 1\over100}= 208\); ⇒ Pr+200r = 20800; ⇒ 20000+200r=20800; ⇒ r = 4% p.a.
SSC CGL 20204)If in 13 years a fixed sum doubles at simple interest, what will be the interest rate per year? (Correct to two decimal places)
7.69%
Principal = Rs. x (let); Interest = Rs. x; ⇒ Rate = \({Interest \times 100\over Principal \times Time }= {{x\times100}\over{x\times 13}} =7.69\)%per annum
SSC CGL 20205)A man buys two watches ‘A’ and ‘B’ at a total cost of ₹800. He sells both watches at the same selling price, and earns a profit of 18% on watch ‘A’ and incurs a loss of 22% on watch ‘B’. Whatare the cost prices of the two watches? (correct to two places after decimal).
A = ₹318.37 and B = ₹481.63
Let C.P. of watch A be Rs. x. C.P. of watch B = Rs.(800 - x); According to the question, \(x\times{118\over100}=(800-x)\times({100-22\over100})\); ⇒ x = Rs. 318.37; C.P. of watch B = 800 - 318.37 = Rs. 481.63
SSC CGL 20206)A sum lent out at compound interest amounts to Rs.1,250 in one year and to Rs.1,458 in 3 years at a certain rate percentage p.a. What is the simple interest on the same sum for \(5{2\over5}\) years at the same rate of interest?
Rs. 500
\(P(1+{r\over100})=1250\)___(1); \(P(1+{r\over100})^3=1458\)_____(2); equation(2) ÷ equation(1); \((1+{r\over100})^2={1458\over1250}\); ⇒ r = 8%;
Calculate P by substituting value of r in equation (1) P = \(31250\over27\); Simple interest = \({31250\over27}\times8\times{27\over5}\over100\) = Rs. 500
SSC CGL 20207)The simple interest on a sum of Rs. 50,000 at the end of two years is Rs.4,000. What would be the compound interest on the same sum at the same rate for the same period ?
Rs. 4,080
Principal(p) = 50000 ; Interest(i) = 4000 ; Time(t) = 2 years ; Rate = \({S.I.\times100\over P\times T} = {4000\times100\over50000\times2} \) = 4% per annum ; Compound interest = \(P[(1+{R\over100})^T-1] =50000[(1+{4\over100})^2 -1]\) = Rs. 4080
SSC CGL 20208)The rate of simple interest on a sum of money is 5% p.a. for the first 4 years, 8% p.a. for the next 3 years and 10% p.a. for the period beyond 7 years. If the simple interest accrued by the sum over a period of 10 years is Rs.1,850, then the sum is :
Rs. 2,500
Simple interest = \(\frac{Principle\times Time\times Rate}{100}\);
Simple interest for 10 years = 1,850;
Simple interest for 4 years at 5% + Simple interest for 3 years at 8% + Simple interest for 3 years at 10% = 1850;
\(\frac{p \times 5 \times 4}{100} + \frac{p \times 8 \times 3}{100} + \frac{p \times 10 \times 3}{100}\) = 1850;
p(20 + 24 + 30) = 185000;
p = 185000/74 = 2500
SSC CGL 20209)Amit borrowed a sum of Rs. 25,000 on simple interest. Bhola borrowed the same amount on compound interest (interest compounded yearly). At the end of 2 years, Bhola had to pay Rs. 160 more interest than Amit. The rate of interest charged per annum is:
8%
For 2 years, Difference between C.I. and S.I. = \(P({R\over100})^2\); ⇒ \(160 = 25000\times({R\over100})^2\); ⇒ R = 8% per annum
SSC CGL 202010)What will be the difference in compound interest on a sum of Rs. 7,800 at 8% p.a. for 1 year, when the interest is paid yearly and half yearly?
Rs. 12.48
For 1 year, C.I. = S.I.; Here, interest = R = 4% per half year; For 2 half-years, C.I. - S.I. = \({PR^2\over10000}= {7800\times4\times4\over10000}\) = Rs. 12.48