A person spends a part of amount of $20,000 for buying. 40% of the remaining amount is given at 6% interest and the rest money is given at 10% interest. If the total interest the person gets is $1250, then what is the amount he used for buying?

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- Aug 12th 2009, 10:06 AM #1

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- Aug 12th 2009, 11:29 AM #2

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- Aug 12th 2009, 12:14 PM #3
My Interpretation

1. A person gets $20,000

2. This person then spends an amount of money

3. 40% of the remainder attracts 6% interest

4. 10% of the remainder (from step 2) attracts 10% interest.

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Let x be the amount he spends and y be the amount which gets interest

$\displaystyle y = 20,000-x $

40% of y gets 6% interest: $\displaystyle 0.4y(1.06)^n$

60% of y gets 10% interest: $\displaystyle 0.6y(1.10)^n$

0.4y(1.06)^n + 0.6y(1.10)^n = 1250

If we assume n is over one period of time (usually annually) so that will cancel

$\displaystyle 0.424y+0.66y = 1250$

$\displaystyle 1.084y = 1250$

$\displaystyle

y = 1153.1365$

$\displaystyle x = 20000-y = 20000-1153.1365 = \$18846.86$

- Aug 12th 2009, 06:49 PM #4

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Hello, bluffmaster.roy.007!

I interpreted it differently . . .

A person spends a part of amount of $20,000 for buying.

40% of the remaining amount is given at 6% interest

and the rest of the money is given at 10% interest.

If the total interest the person gets is $1250,

then what is the amount he used for buying?

The person has $20,000.

He spend $\displaystyle x$ dollars for buying.

He has $\displaystyle 20,\!000-x$ dollars remaining.

40% of this remainder is: .$\displaystyle 0.40(20,\!000-x)$ dollars.

This earns 6% interest: .$\displaystyle I_1 \:=\:(0.06)(0.40)(20,\!000-x)\:=\:480 - 0.024x$

60% of the remainder is: .$\displaystyle 0.60(20,\!000-x)$ dollars.

This earns 10% interest: .$\displaystyle I_2 \:=\:(0.10)(0.60)(20,\!000-x) \:=\:1200 - 0.06x$

The total interest is $1250: .$\displaystyle (480-0.024x) + (1200 - 0.06x) \:=\:1250$

We have: .$\displaystyle 0.084x \:=\:430 \quad\Rightarrow\quad x \:=\:\frac{430}{0.084} \:=\:5119.047619$

Therefore, he used $5,119.05 for buying.

- Aug 18th 2009, 01:46 PM #5

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## alternate solution......

Mr sorobon is rite..........

lets see how eazy it is..........consider x be the amount remainin...

that is x=20,000-amount used for buying.

40% of remaining amount x gets 6%interest

that is......(0.4)(0.06)(x)

and for second interest (0.6)(0.1)(x)

together they make 1250$=0.024x+0.06x

x=1250/0.084=14880.1

so amount used for buying is 20,000-x

and that is 5119.9$....