1. A sum of $24000 is deposited in a bank in such a way that part of the sum receives interest at 4% p.a. and the remainder at 6%p.a. The total annual interest received from the sum of money is $1010. Calculate the amount of money in each of the two parts of the sum. [ Ans: interest rate at 4% : $21500, interest rate at 6%: $2500]
2. In a department store, 70% of a product are sold at a profit of 40% and the rest are sold at a loss of 15%. What is the profit per cent if every single piece of the product has been sold? (Assume that the cost price of the product is a constant.) [Ans. 23.5%]
Thank you!
Interest problems
2009-07-11 2:35 am
回答 (2)
2009-07-11 4:09 am
✔ 最佳答案
(1)Let $X is at 4% and $(24000-X) at 6%
X * 4% + (24000 - X) * 6% = 1010
0.04X + 1440 - 0.06X = 1010
0.02X = 430
X = 21500
So $21500 is with interest rate 4%
For 6% it is 24000 - 21500 = $2500
(2)
Let X be the total quantity of products
Let $Y be the cost of a product
Total cost of product = $XY
Sales of product = X*70% * Y*(1+40%) + X*30% * (1-15%)
= (0.7X)(1.4Y) + (0.3X)(0.85Y)
= $1.235XY
Overall profit percent = (1.235XY - XY)/XY * 100%
= 23.5%
2009-07-11 4:45 am
(1)
Let Xbe the amount of money at the interest rate of 4%
Then the formula would be :
0.04X + 0.06(24000 - X) = 1,010
=>0.04X + 1440 - 0.06X = 1,010
=>0.02X = 430
=>X = 21,500
Therefore the answers are :
$21,500 was deposited at the interest rate of 4%, and
$2,500 ($24,000 -$ 21,500) was at 6%.
(2)
As it was given that the cost of the product was at a constant amount, the overall profit % should be the weighted average of the 40% profit and the 15% loss.
0.7 * 40% + 0.3 *-15%
=28% - 4.5%
=23.5%
Therefor the answer is 23.5%
Let Xbe the amount of money at the interest rate of 4%
Then the formula would be :
0.04X + 0.06(24000 - X) = 1,010
=>0.04X + 1440 - 0.06X = 1,010
=>0.02X = 430
=>X = 21,500
Therefore the answers are :
$21,500 was deposited at the interest rate of 4%, and
$2,500 ($24,000 -$ 21,500) was at 6%.
(2)
As it was given that the cost of the product was at a constant amount, the overall profit % should be the weighted average of the 40% profit and the 15% loss.
0.7 * 40% + 0.3 *-15%
=28% - 4.5%
=23.5%
Therefor the answer is 23.5%
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