# Thread: Simple & Compound interest problems (Guru level) Originally Posted by sunilcyborg 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 %.  Reply With Quote

2. Originally Posted by sunilcyborg 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  Reply With Quote

3. Please let me know if these questions fall below or above GMAT level   Reply With Quote

4. 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.  Reply With Quote

5. Originally Posted by sunilcyborg 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   Reply With Quote

6. 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.  Reply With Quote

7. Originally Posted by hardikrs 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%.  Reply With Quote

8. Originally Posted by hardikrs 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.  Reply With Quote

9. Originally Posted by paul2432 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  Reply With Quote