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Thread: Simple & Compound interest problems (Guru level)

  1. #21
    GMAT TEST EXPERTS MBAchase's Avatar
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    Quote Originally Posted by sunilcyborg View Post
    Help Anyone!


    A watermelon weighs 5000gm, 99% of its weight is water. It is kept in a drying room and after some time it turns out that it is only 98% water by weight. What is its weight now?

    1) 2500 gm
    2) 4500 gm
    3) 4950 gm
    4) None of these
    solution: answer is 1) 2500 gm

    Explanation :
    since when drying only the quantity of water will change but the pulp would remain same.
    so initally 99% water : 4950 gm , 1% pulp = 50 gm because total weight is 5000gm
    after drying 98% water = ? (we don't know the weight after drying)
    2% pulp = 50 gm (as the weight of pulp would not change)
    thus for calculating total weight we know that pulp is 2% and 50 gm thus 2% of what is equal to 50 gm
    thus x*2/100 =50
    => x =2500 gm
    NOTE: remember these are the problem related to base change in %. Later case we don't know the base.
    so Always remember what is the base over what we want to calculate %.


  2. #22
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    Quote Originally Posted by sunilcyborg View Post
    1 more to go guys

    A man borrows Rs 1200 in order to buy a new house and agrees to pay back a fixed sum of Rs 300 at the end of each subsequent year, If compound interest is charged at the rate of 5% per year, how much remains to be paid off at the end of fourth year?
    Solution:
    Dear this is not a GMAT level question. so please don't put these type of questions.

    Explanation:

    1200
    1) after one yr interest paid 1200 * .05= 60 Rs and Principal paid 300 - 60=240
    thus P remaining = 1200 - 240 = 960

    2)
    after 2nd yr interest paid 960*.05= 48 Rs and Principal paid =300 -48 = 252 thus P remaining = 960 - 252 = 708

    3)
    after 3rd yr interest paid 708 * .05 = 35.40 Rs and Principal paid 300 - 35.40 =264.60 thus P remaining = 708 - 264.60 = 443.40

    4)
    after 4th yr interest paid 443.40 * .05= 22.17 Rs and Principal paid 300 -22.17 = 277.83 thus
    P remaining = 443.40 - 277.83 = 165.57 Rs

    thus this is the amt he has to paid after 4th yr.
    If you want to calculate the 5th installment then
    that is 165.57 * (1.05) = 173.8485 Rs

  3. #23
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    Please let me know if these questions fall below or above GMAT level

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    I wanted 2 add 1 more thing.. I knew the above problem had a tedious solution. I just thought may b I could find a shorter method to solve it.

  5. #25
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    Quote Originally Posted by sunilcyborg View Post
    I wanted 2 add 1 more thing.. I knew the above problem had a tedious solution. I just thought may b I could find a shorter method to solve it.
    Dear,
    Base change questions always come in GMAT , so be familiar with these question. they are tricky and have traps.
    But in case of SI and CI very simple questions come so don't need to go for higher level of interest based question



  6. #26
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    MBA chase, can you please explain this in detail. thanks

    The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent
    Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

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    Quote Originally Posted by hardikrs View Post
    MBA chase, can you please explain this in detail. thanks

    The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent
    Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

    Dear Hardikrs,
    one year SI is pr/100
    If we calculate the CI for two yr the value of it is
    P ( 1 +r/100)^2 - p = P(2r/100 + (r/100)^2)

    and SI = 2PR/100
    thus difference of CI and SI is p(r/100)^2 =(Pr/100)*(r/100)
    thus so this is nothing but r% of 1st year interest or interest on interest.
    so 1st yr interest is 400 and difference is 32 thus
    r% of 400 is 32 thus r is 8%.



  8. #28
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    Quote Originally Posted by hardikrs View Post
    MBA chase, can you please explain this in detail. thanks

    The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent
    Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

    Dear Hardikrs,
    one year SI is pr/100
    If we calculate the CI for two yr the value of it is
    P ( 1 +r/100)^2 - p = P(2r/100 + (r/100)^2)

    and SI = 2PR/100
    thus difference of CI and SI is p(r/100)^2 =(Pr/100)*(r/100)
    thus so this is nothing but r% of 1st year interest or interest on interest.
    so 1st yr interest is 400 and difference is 32 thus
    r% of 400 is 32 thus r is 8%.
    and r is 8% i = 400 and t =1 thus P is 5000.


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    Quote Originally Posted by paul2432 View Post
    This is incorrect because the principal is reduced after the first payment. Here is how to solve it.

    Let:
    I1=interest paid in the first payment
    I2=interest paid in the second payment
    P1=principal paid in the first payment
    P2=principal paid in the second payment

    Because the payments are equal:
    I1 + P1 = I2 + P2

    Because all the principal is paid:
    P1 + P2 = 550

    First payment interest is on the full loan:
    I1 = 550 x 0.2 = 110

    Second payment interest is only on the remaining principal:
    I2 = (550-P1) x 0.2

    Substituting:
    110 + P1 = (550 - P1)(0.2) + (550-P1)
    110 + P1 = 110 - 0.2P1 + 550 - P1
    2.2P1 = 550
    P1 = 250
    Payment = 250 + 110 = 360

    Check:
    P2 = 550 - P1 = 550 - 250 = 300
    I2 = 0.2 x 300 = 60
    Payment = 300 + 60 = 360

    Paul


    Hi i having confusion in this part
    Second payment interest is only on the remaining principal:
    I2 = (550-P1) x 0.2

    because the calculation is based on C.I . The statment should be like this Second payment interest is only on the remaining principal:
    I2 = (550-P1+110) x 0.2.........because the intrest of first year has to be added in to the 2nd year principle ammout

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