What annual payment will discharge a debt of Rs. 1740 due in 5 years, the rate being 8% per annum?
A
Rs. 360A
Rs. 360B
Rs. 300B
Rs. 300C
Rs. 320C
Rs. 320D
Rs. 340D
Rs. 340
Let the annual instalment be Rs. $$x$$. Then,
$$[x+(\cfrac{x\times 4\times 8}{100})]+[x+(x+(\cfrac{x\times 3\times 8}{100})]$$
$$+[x+(\cfrac{x\times 2\times 8}{100})]+[x+(\cfrac{x\times 1\times 8}{100})]+x = 1740$$
$$\Rightarrow \cfrac{33x}{25}+\cfrac{31x}{25}+\cfrac{29x}{25}+\cfrac{27x}{25}+x = 1740$$
$$\Rightarrow x = 300$$
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Correct Answer: B
Solution :
Let the annual instalment be Rs. x. Then, \[\left[ x+\left( \frac{x\times 4\times 8}{100} \right) \right]+\left[ x+\left( \frac{x\times 3\times 8}{100} \right) \right]\] \[+\left[ x+\left( \frac{x\times 2\times 8}{100} \right) \right]+\left[ x+\left( \frac{x\times 1\times 8}{100} \right) \right]+x=1740\]or \[\frac{33x}{25}+\frac{31x}{25}+\frac{29x}{25}+\frac{27x}{25}+x=1740\] or \[x=300\]
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Page 2
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Correct Answer: C
Solution :
Let sum =x, \[S.I.=Rs.\text{ }6000,\]Time = 10 years. Rate \[=\left( \frac{100\times 6000}{x\times 10} \right)=\left( \frac{60000}{x} \right)%\] S.I. for last 5 years \[=Rs.\left( \frac{x\times 5\times 60000}{x\times 100} \right)=Rs.3000\] S.I. for last 5 years \[=Rs.\left( 3x\times 5\times \frac{60000}{x\times 100} \right)\] \[=Rs.9000\] \[\therefore \] Total interest \[=\text{ }Rs.12000.\]
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Page 3
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Correct Answer: B
Solution :
\[b=\frac{a\times R\times T}{100}\] or \[RT=\frac{100b}{a}\] ?..(i) and \[x=\frac{b\times R\times T}{100}\] or \[RT=\frac{100c}{b}\] ?.(ii) Equating (i) and (ii), we have \[\frac{100b}{a}=\frac{100c}{b}\]or \[{{b}^{2}}=ac\]
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Page 4
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Correct Answer: A
Solution :
Not available
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Page 5
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Correct Answer: C
Solution :
Not available
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Page 6
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Correct Answer: A
Solution :
Not available
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Page 7
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Correct Answer: A
Solution :
Let the money lent at \[8%\]be Rs. x. Then, \[\frac{x\times 8\times 1}{100}+\frac{(15500-x)\times 6\times 1}{100}=1060\] or \[2x+93000=106000\] or \[x=6500\]
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Page 8
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Correct Answer: D
Solution :
Let the sum at 5% be Rs. x. Then, \[\frac{x\times 5\times 3}{100}+\frac{(15500-x)\times 8\times 3}{100}=3000\] or \[x=8000\] or \[\frac{Money\,at\,5%}{Money\,at\,8%}=\frac{8000}{(15500-8000)}\] \[=\frac{8000}{7500}=\frac{16}{15}\]
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Page 9
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Correct Answer: C
Solution :
Let total capital be x. Then, \[\left( \frac{x}{3}\times \frac{7}{100}\times 1 \right)+\left( \frac{x}{4}\times \frac{8}{100}\times 1 \right)+\left( \frac{5x}{12}\times \frac{10}{100}\times 1 \right)\] \[=5610\] or \[\frac{7x}{300}+\frac{x}{50}+\frac{x}{24}=5610\] or \[51x=(5610\times 600)\] or \[x=\left( \frac{5610\times 600}{51} \right)=66000\]
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Page 10
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Correct Answer: C
Solution :
Let the amounts invested by x, y, z respectively. Then, \[\frac{x\times 2\times 5}{100}=\frac{y\times 3\times 5}{100}=\frac{z\times 4\times 5}{100}=k\] \[\therefore \] \[x=10k,y=\frac{20}{3}k,\] and \[z=5k\] So \[x:y:z=10k:\frac{20}{3}k:5k\] \[=30:20:15\] \[=6:4:3\]
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Page 11
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Correct Answer: D
Solution :
Not available
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Page 12
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Correct Answer: B
Solution :
Not available
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Page 13
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Correct Answer: A
Solution :
Not available
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Page 14
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Correct Answer: C
Solution :
Not available
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Page 15
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Correct Answer: C
Solution :
Not available
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Page 16
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Correct Answer: C
Solution :
Not available
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Page 17
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Correct Answer: B
Solution :
Not available
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Page 18
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Correct Answer: B
Solution :
Not available
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Page 19
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Correct Answer: B
Solution :
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Page 20
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Correct Answer: C
Solution :
Not available
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Page 21
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Correct Answer: B
Solution :
Let the savings be X and Y and the rates of simple interest be 5-x; and 4x respectively. Then, \[X\times 5x\times \frac{1}{2}\times \frac{1}{100}=Y\times 4x\times \frac{1}{2}\times \frac{1}{100}\] or \[\frac{X}{Y}=\frac{4}{5}.X:Y=4:5\]
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Page 22
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Correct Answer: B
Solution :
Sum \[=Rs.\left( \frac{100\times 12000}{3\times t5} \right)=Rs.80000\] Assume \[=Rs.\left[ 80000\times {{\left( 1+\frac{5}{100} \right)}^{3}} \right]\] \[=Rs.\,\,92610\] \[\therefore \] C.I. \[=Rs.(92610-80000)\] \[=Rs.12610\]
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Page 23
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Correct Answer: B
Solution :
C.I. \[=Rs.\left[ 8000\times {{\left( 1+\frac{10}{100} \right)}^{2}}-8000 \right]\] \[=Rs.1680\] S.I. \[=Rs.\left( \frac{8000\times 10\times 2}{100} \right)=Rs.1600\] Gain \[=(C.I.)-(S.I.)\] \[=Rs.\,(1680-1600)=Rs.80\]
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Page 24
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Correct Answer: C
Solution :
Amount \[=Rs.\left[ 5600\times \left( 1+\frac{10}{100} \right)\times \left( 1+\frac{\frac{1}{2}\times 10}{100} \right) \right]\] \[=Rs.\left( 5600\times \frac{11}{10}\times \frac{21}{20} \right)=Rs.6468\] \[\therefore \] C.I. \[=-Rs.(6468-5600)=Rs.868\]
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Page 25
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Correct Answer: B
Solution :
Let the principal at the end of first year be Rs. x. Then \[\frac{x\times 10\times 1}{100}=1320\] or \[x=13200\] Now, let the original principal be Rs. P. Then. amount after 1 year \[=P+\frac{P\times 10\times 1}{100}=\frac{11P}{10}\] \[\therefore \] \[\frac{11P}{10}=13200\] or \[P=\left( \frac{13200\times 10}{11} \right)=Rs.12000\]
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Page 26
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Correct Answer: C
Solution :
Interest on \[Rs.\text{ }10580\]for 1 year \[=Rs.(12167-10580)\] \[=Rs.1587\] \[\therefore \] Rate \[=\left( \frac{100\times 1587}{10580} \right)%=15%\]
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