Simple interest


  1. ₹800 becomes ₹956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will ₹800 become in 3 years ?









  1. View Hint View Answer Discuss in Forum

    We know that ,
    S.I. = Amount - Principle = 956 – 800 = Rs. 156

    ∴ Rate =
    S.I. × 100
    Principal × Time

    R =
    156 × 100
    = 6.5% per annum
    800 × 3

    ∴ New rate = 6.5 + 4 = 10.5%

    Correct Option: C

    We know that ,
    S.I. = Amount - Principle = 956 – 800 = Rs. 156

    ∴ Rate =
    S.I. × 100
    Principal × Time

    R =
    156 × 100
    = 6.5% per annum
    800 × 3

    ∴ New rate = 6.5 + 4 = 10.5%
    ∴ SI =
    Principal × Time × Rate
    100

    SI =
    800 × 3 × 10.5
    = ₹ 252
    100

    ∴ Amount = Principle + SI = 800 + 252 = ₹ 1052


  1. A person borrows ₹5,000 for 2 years at 4% per annum simple interest. He immediately
    lends it to another person at 61% per annum simple interest for 2 years.
    4
    His gain in the transaction is









  1. View Hint View Answer Discuss in Forum

    Here , P = ₹ 5000 , R = 4% , T = 2 years
    Case I :

    SI =
    5000 × 2 × 4
    = ₹ 400
    100

    Case II :
    Here , P = ₹ 5000 , T = 2 years , R =
    25
    %
    4

    SI =
    5000 × 25 × 2
    = ₹ 625
    100 × 4

    Correct Option: C

    Here , P = ₹ 5000 , R = 4% , T = 2 years
    Case I :

    SI =
    5000 × 2 × 4
    = ₹ 400
    100

    Case II :
    Here , P = ₹ 5000 , T = 2 years , R =
    25
    %
    4

    SI =
    5000 × 25 × 2
    = ₹ 625
    100 × 4

    ∴ Gain = ₹ (625 – 400) = ₹ 225



  1. In what time will 72 become ₹81 at 61% per annum simple interest ?
    4









  1. View Hint View Answer Discuss in Forum

    Let the time be t years.
    Simple Interest = Amount - Principle = ₹(81 – 72) = ₹9
    We know that ,

    SI =
    P × R × t
    100

    9 =
    72 × 25 × t
    4 × 100

    Correct Option: A

    Let the time be t years.
    Simple Interest = Amount - Principle = ₹(81 – 72) = ₹9
    We know that ,

    SI =
    P × R × t
    100

    9 =
    72 × 25 × t
    4 × 100

    ⇒ t =
    9 × 400
    = 2yrs
    72 × 25


  1. What annual instalment will discharge a debt of ₹6450 due in 4 years at 5% simple interest ?









  1. View Hint View Answer Discuss in Forum

    Let each instalment be y Then,

    y + y × 5 × 1 + y +y × 5 × 2 + y +y × 5 × 3 + y = 6450
    100100100

    y + y + y + y + y + 3y + y = 6450
    201020

    21y
    +
    11y
    +
    23y
    + y = 6450
    201020

    21y + 22y + 23y + 20y
    = 6450
    20

    86y
    = 6450
    20

    ⇒ y =
    6450 × 20
    = ₹ 1500
    86

    Second method to solve this question :
    Here , A = ₹ 6450 , T = 4 years , R = 5%
    Equal instalment =
    A × 200
    T[200 + (T - 1) × R]

    Correct Option: A

    Let each instalment be y Then,

    y + y × 5 × 1 + y +y × 5 × 2 + y +y × 5 × 3 + y = 6450
    100100100

    y + y + y + y + y + 3y + y = 6450
    201020

    21y
    +
    11y
    +
    23y
    + y = 6450
    201020

    21y + 22y + 23y + 20y
    = 6450
    20

    86y
    = 6450
    20

    ⇒ y =
    6450 × 20
    = ₹ 1500
    86

    Second method to solve this question :
    Here , A = ₹ 6450 , T = 4 years , R = 5%
    Equal instalment =
    A × 200
    T[200 + (T - 1) × R]

    Equal instalment =
    6450 × 200
    4[200 + (4 - 1) × 5]

    Equal instalment =
    6450 × 200
    4 × 215

    Equal instalment =
    6450 × 200
    4 × 215

    Equal instalment =
    6450 × 50
    215

    Equal instalment = ₹ 1500



  1. A sum of money lent out at simple interest amounts to 720 after 2 years and to 1020 after a further period of 5 years. The sum is :









  1. View Hint View Answer Discuss in Forum

    As per the given in question ,
    Principal + SI for 2 years = ₹720 .... (i)
    Principal + SI for 7 years = ₹1020 .....(ii)
    Subtracting equation (i) from (ii) get,
    SI for 5 years = (1020 – 720) = ₹300
    ∴ SI for 2 years = 300 × ( 2 ÷ 5 ) = ₹120
    ∴ Principal = Amount - SI = (720 – 120) = ₹600
    Second method to solve this question :
    Here , A2 = ₹ 1020 , T1 = 2 years , A1 = ₹ 720 , T2 = 7 years

    P =
    A2T1 - A1T2
    T1 - T2

    Correct Option: B

    As per the given in question ,
    Principal + SI for 2 years = ₹720 .... (i)
    Principal + SI for 7 years = ₹1020 .....(ii)
    Subtracting equation (i) from (ii) get,
    SI for 5 years = (1020 – 720) = ₹300
    ∴ SI for 2 years = 300 × ( 2 ÷ 5 ) = ₹120
    ∴ Principal = Amount - SI = (720 – 120) = ₹600
    Second method to solve this question :
    Here , A2 = ₹ 1020 , T1 = 2 years , A1 = ₹ 720 , T2 = 7 years

    P =
    A2T1 - A1T2
    T1 - T2

    P =
    1020 × 2 - 720 × 7
    2 - 7

    P =
    2040 - 5040
    - 5

    P =
    - 3000
    - 5

    P = ₹ 600