can u solve this.... Also show the working..?

Question

1. A house was sold at a gain of 10%. Had it been sold for Rs. 3000 more the gain would have been 15%. find the cost of the house?

2. If the cost price of 20 eggs is equal to selling price of 25 eggs. Find the loss percentage?

3. In 4 years Rs. 6000 amounts to Rs. 8000. In what time will Rs. 525 amount to Rs. 700 at the same rate?

Answer 1

1)
C.P. of the house = Rs. x
Profit is it is sold at 15 % = Rs. 0.15x
Profit is it is sold at 10 % = Rs. 0.1x
0.15x - 0.1x = 3000
So cost of house, Rs. x = Rs. 60, 000

2)
C.P. of 20 eggs = Rs. x.
S.P. of 25 eggs = Rs. x.
C.P. of 1 egg = Rs. x/20.
S.P. of 1 egg = Rs. x/25.
Profit % = [(x/25 - x/20) / (x/20)] x 100 = -20
- sign means: loss
So, loss % = 20

3)
A = P + PRT
A = Amount; P = Principal; R = (Annual) Rate of simple interest; T = Time in years

Here, P = 6000, A = 8000, T = 4, R = ?
PRT = A - P = 8000 - 6000 = 2000
R = 2000/(PT) = 2000/(6000 x 4) = 1/12

Now, P = 525, A = 700, R = 1/12, T = ?
T = (A - P)/(PR) = (700 - 525)/(525/12) = 4

Answer 2

1. A house was sold at a gain of 10%. Had it been sold for Rs. 3000 more the gain would have been 15%. find the cost of the house?

3000 is 5% of the cost of the house and so 3000 x 20 = 60,000 is the cost of the house.

2. If the cost price of 20 eggs is equal to selling price of 25 eggs. Find the loss percentage?

Loss = Sale Price - Cost price

To get a clear perspective on such problems, it is good to work with some figures. Let 1 rupee be the cost of an egg. So, 20 eggs cost 20 rupees and if the person is forced to sell 25 eggs for 20 rupees, the selling price of an egg is 80 paise. Loss is 20 paise and the percentage is 20%.

3. In 4 years Rs. 6000 amounts to Rs. 8000. In what time will Rs. 525 amount to Rs. 700 at the same rate?

8000 - 6000 = 2000

2000 / 6000 = 1/3

700 - 525 = 175

175 / 525 = 1/3

Thus the time remains same.

Answer 3

1. Let x be the cost of the house originally, y be the cost of the house at 10% gain:
(NB: * denotes multiplication)

y = 1.10*x (since 10% gain is the same as multiplying by 1.1)
3000 + y = 1.15*x (second part of the information)

Solve simultaneously, by subtracting the two equations:
3000 = 0.05*x
x = 3000 / 0.05 = 3000*20 = 60000
i.e. original cost of house is Rs. 60000.

(You can check this too: 10% gain onto 60000 is 66000. 3000 more is 69000. 69000 / 60000 = 1.15, which is 15% gain.)

2. 20*(cost price) = 25*(sell price)
sell price = 20/25 * (cost price)
= 0.80 * (cost price)
i.e. sell price is 80% of cost price, which is a 20% loss percentage.

3. In 4 years, Rs. 2000 interest has been added to the Rs. 6000, which means interest rate is [(2000/6000)/4] per annum (dividing by 4 because of the 4 years). Hence, interest rate is 1/12 (easiest to leave as a fraction).

For 525 to amount to 700, we need interest of 175 from the investment of 525. We have that the interest rate is 1/12. The formula for simple interest is
interest = (initial amount)*(interest rate)*(time in years)
175 = 525*(1/12)*time
then, time = 175 / 525 * 12 = 4 years.

Hope you understood that (and that the answers are correct), I don't know at what your level of understanding of maths is. I can explain it in more detail if this is too confusing.