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Quantitative Aptitude > Interest

SIMPLE INTEREST MCQs

Total Questions : 234 | Page 3 of 24 pages
Question 21. A money lender finds that due to fall in the annual rate of interest 8% to 7$3/4$% , his yearly income diminishes by Rs.61.50. His capital is
  1.    Rs.23800
  2.    Rs.22400
  3.    Rs.26000
  4.    Rs.24600
 Discuss Question
Answer: Option D. -> Rs.24600
Answer: (d)Difference in rate= $(8 - 7{3}/4)% = 1/4$%Let the capital be Rs.x.$1/4$% of x = 61.50x = 61.50 × 100 × 4 = Rs.24600
Question 22. A person borrows Rs.5,000 for 2 years at 4% per annum simple interest. He immediately lends it to another person at 6$1/4$% per annum simple interest for 2 years. His gain in the transaction is
  1.    Rs.450
  2.    Rs.112.50
  3.    Rs.150
  4.    Rs.225
 Discuss Question
Answer: Option D. -> Rs.225
Answer: (d)Using Rule 1,Case I : S.I. = ${5000 × 2 × 4}/100$ = Rs.400Case II :S.I. = ${5000 × 25 × 2}/{100 × 4}$ = Rs.625Gain = Rs.(625 - 400) = Rs.225
Question 23. A sum of money amounts to Rs.850 in 3 years and to Rs.925 in 4 years at some rate of simple interest. The sum is :
  1.    Rs.600
  2.    Rs.550
  3.    Rs.700
  4.    Rs.625
 Discuss Question
Answer: Option D. -> Rs.625
Answer: (d)Interest for 1 year= Rs.(925 - 850) = Rs.75If a sum becomes $a_1$ in $t_1$ years and $a_2$ in $t_2$ years then rate of interest= ${100(a_2 - a_1)}/({a_1t_2 - a_2t_1})%$= ${100(925 - 850)}/{850 × 4 - 3 × 925} = 7500/625$ = 12%Principal = ${SI × 100}/{\text"Time × Rate"$= ${75 × 100}/{1 × 12}$ = Rs.625Using Rule 12,P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$= ${925 × 3 - 850 × 4}/{3 - 4}$= ${2775 - 3400}/{-1}$= ${- 625}/{- 1}$ = Rs.625
Question 24. In how many years will a sum of Rs.3,000 yield a simple interest of Rs.1,080 at 12% per annum ?
  1.    2$1/2$ years
  2.    3 years
  3.    3$1/2$ years
  4.    2 years
 Discuss Question
Answer: Option B. -> 3 years
Answer: (b)Using Rule 1,Time = ${SI × 100}/{\text"Principal × Rate"$= ${1080 × 100}/{3000 × 12} = 3$ years
Question 25. A lends Rs.2500 to B and a certain sum to C at the same time at 7% annual simple interest. If after 4 years, A altogether receives Rs.1120 as interest from B and C, the sum lent to C is
  1.    Rs.6500
  2.    Rs.700
  3.    Rs.1500
  4.    Rs.4000
 Discuss Question
Answer: Option C. -> Rs.1500
Answer: (c)Using Rule 1,Let the sum lent to C be xAccording to the question,${2500 × 7 × 4}/100 + {x × 7 × 4}/100 = 1120$or 2500 × 28 + 28x = 112000or 2500 + x = 4000or x = 4000 - 2500 = 1500
Question 26. A sum of money at some rate of simple interest amounts to Rs.2,900 in 8 years and to Rs.3,000 in 10 years. The rate of interest per annum is
  1.    2$1/2$%
  2.    4%
  3.    2%
  4.    3%
 Discuss Question
Answer: Option C. -> 2%
Answer: (c)Principal + interest for 8 years= Rs.2900... (i)Principal + interest for 10 years = Rs.3000 ... (ii)Subtracting equation (i) from (ii)Interest for 2 years = Rs.100Interest for 8 years= $100/2 × 8$ = Rs.400From equation (i),Principal = Rs.(2900 - 400) = Rs.2500Rate = ${S.I × 100}/{\text"Time × Principal"}$= ${400 × 100}/{8 × 2500} = 2%$Using Rule 12,R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100= $({2900 - 3000}/{3000 × 8 - 2900 × 10})$ × 100=$({- 100}/{24000 - 29000}) × 100$= ${-100}/{-5000}$ × 100 = 2%
Question 27. What sum will amount to Rs.7000 in 5 years at 3$1/3$% simple interest ?
  1.    Rs.6500
  2.    Rs.6300
  3.    Rs.5000
  4.    Rs.6000
 Discuss Question
Answer: Option D. -> Rs.6000
Answer: (d)Using Rule 1,P = ${A × 100}/{100 + r × t}$=${7000 × 100}/{100 + 10/3 × 5}$= ${7000 × 100 × 3}/350$ = Rs.6000
Question 28. A person deposited Rs.400 for 2 years, Rs.550 for 4 years and Rs.1,200 for 6 years. He received the total simple interest of Rs.1,020. The rate of interest per annum is
  1.    5%
  2.    10%
  3.    20%
  4.    15%
 Discuss Question
Answer: Option B. -> 10%
Answer: (b)Using Rule 1,Let the rate of interest be R per cent per annum.${400 × 2 × R}/100 + {550 × 4 × R}/100$+ ${1200 × 6 × R}/100 = 1020$8R + 22 R +72 R = 1020102 R= 1020R = $1020/102$ = 10%
Question 29. If the simple interest on a certain sum of money for 15 months at 7$1/2$% per annum exceeds the simple interest on the same sum for 8 months at 12$1/2$% per annum by Rs.32.50, then the sum of money (in ) is :
  1.    312.50
  2.    312
  3.    3120.50
  4.    3120
 Discuss Question
Answer: Option D. -> 3120
Answer: (d)Using Rule 1,Let the sum be x.Using formula, I = $\text"PRT"/100$ we have${x × 15/12 × 15/2}/{100 - x} - {x × 8/12 × 25/2}/100$= 32.50${25x}/2400$ = 32.50$x = {32.50 × 2400}/25$ = 3120Required sum = Rs.3120
Question 30. What sum of money will amount to Rs.520 in 5 years and to Rs.568 in 7 years at simple interest ?
  1.    Rs.120
  2.    Rs.400
  3.    Rs.220
  4.    Rs.510
 Discuss Question
Answer: Option B. -> Rs.400
Answer: (b)Simple interest for 2 years= Rs.(568 - 520) = Rs.48Interest for 5 years= Rs.$48/2 × 5$ = Rs.120Principal = Rs.(520 - 120) = Rs.400Using Rule 12,P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$=$({568 × 5 - 520 × 7}/{5 - 7})$= $({2840 - 3640}/{-2})$=${- 800}/{- 2}$ = Rs.400

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