Quantitative Aptitude: Simple/Compound Interest Set 13

  1. Simple interest on a certain amount is 4/25 of the principal. If the numbers representing the rate of interest in percent and time in years be equal, Find the time, for which the principal is lent out.
    5 years
    8 years
    10 years
    4 years
    2 years
    Option D
    Rate = Time = t
    New Time , t = (4p*100)/(25*t*p)
    => t = 4 years

     

  2. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 3 years on simple interest at the same rate of interest and received Rs. 3800 in all from both of them as interest.What is the rate of interest per annum.
    5%
    20%
    15%
    10%
    8%
    Option B
    (5000*R*2)/100 + (3000*R*3)/100 = 3800
    => 100R + 90R = 3800
    => R = 20%

     

  3. Lakshman gave Rs. 1200 on loan. Some amount he gave at 4% per annum on simple interest and remaining at 5% per annum on simple interest. After two years, he got Rs. 110 as interest. Find the amounts given at 4% and 5% per annum on simple interest are, respectively.
    Rs.500 and Rs.700
    Rs.120 and Rs.180
    Rs.550 and Rs.640
    Rs.320 and Rs.450
    None of these
    Option A
    Let the amount be x and (1200-x).
    (x*4*2)/100 + ((1200-x)*5*2)/100 = 110
    => 8x/100 + (12000 – 10x)/100 = 110
    => -2x + 12000 = 11000
    => 1000/2 = 500= x
    The required amounts are 500 and 700.

     

  4. A’s Share at the end of 3 years may equal to B’s share at the end of 5 years dividing the Rs.4199 between A and B, compound interest being at 10%.What is the present share of B.
    Rs.1900
    Rs.1000
    Rs.1150
    Rs.2200
    Rs.1500
    Option A
    A’s share after 3 years = B’s share after 5 years
    A’s present share / B’s present share= (1+10/100)^5/(1+10/100)^3 = 121/100
    A’s present share = (121*4199)/221 = Rs.2299
    B’s present share = (100*4199)/221 = Rs.1900

     

  5. Rahul borrowed a certain sum from Harish at a certain rate of simple interest for 2 years. He lent this sum to Shilpa at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
    20%
    30%
    40%
    10%
    50%
    Option C
    Let sum be x.
    Simple interest on x for 2 years = Rs.2000
    SI= P*R*T/100
    => 2000= x*R*2/100
    => 100000=xR——-(1)
    Compound Interest on x for 2 years = 2400 P(1+R/100)^t – P = 2400
    =>x(1+R/100)^2 – x = 2400
    => 2xR/100 + xR^2/100 = 2400——(2)
    On substituting (1) and (2), we get
    R = 40%

     

  6. If a sum of Rs. 15000 is placed at compound interest for 3 years while rate of interest for the first, second and third years is 6%, 8% and 10% respectively.Find the amount?
    Rs.15,889.0
    Rs.18,889.2
    Rs.2,225
    Rs.1,578.6
    None of these
    Option B
    Amount after 3 years,
    = 15000(106/100)(108/100)(110/100)
    =Rs.18,889.2

     

  7. A sum of Rs. 5000 was taken as a loan and the amount is to be repaid in two equal annual installments. If the rate of interest be 10% compounded annually then find the value of each installment .
    Rs.2000
    Rs.1859.4
    Rs.1550.25
    Rs.2330.5
    Rs.2880.95
    Option E
    Let x be the annual payment.
    X due to 1 year + x due to 2nd year = 5000
    => x/(11/10)^1 + x/(11/10)^2 = 5000
    => x=2880.95

     

  8. Find the compound interest on a principal amount of Rs.3000 after 2 years, if the rate of interest for the 1st year is 5% and for the 2nd year is 7%.
    Rs.3500
    Rs.4255
    Rs.2488
    Rs.3741
    None of these
    Option D
    CI= 3000(105/100)(107/100)-3000
    =6741-3000=3741

     

  9. The amount is increased by 40% in 4 years at simple interest. What will be the compound interest of Rs. 20,000 after 2 years at the same rate?
    Rs.4,550
    Rs.2,,000
    Rs.4,200
    Rs.3,520
    Rs.1,150
    Option C
    Let P = Rs.100
    Simple Interest = Rs. 40
    Rate of interest=(100×SI)/PT =(100×40)/(100×4)=10% per annum
    Now, P = Rs.20,000
    T = 2 years
    R = 10%
    Amount after 2 years =P(1+R/100)^t
    =20000(1+10/100)^2
    =20000(110/100)^2
    =20000(11/10)^2 =24,200
    Compound Interest = Rs.24,200 – Rs.20,000 = Rs.4,200

     

  10. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Rs.2. Find the sum.
    Rs.450
    Rs.720
    Rs.980
    Rs.800
    Rs.600
    Option D
    P(R/100)^2 = 2
    =>P(5/100)^2 = 2
    => P(1/400)= 2
    =>P = Rs.800

     


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