# Thread: algebra problem

1. ## algebra problem

Please can anyone solve the following questions and show working pls.?

1. A man spends 75% of his income, when his income is increased by 20%, he increases his expenditure by 10%. By how much per cent are his savings increased?

2. The marked price of a watch is Rs. 400. After allowing a discount of 25% on the marked price, there was a loss of Rs. 20. Determine the loss per cent.

3. The average of the squares of five consecutive positive integers is 66. Find the average of these five integers.

2. Hi

The first one
1. A man spends 75% of his income, when his income is increased by 20%, he increases his expenditure by 10%. By how much per cent are his savings increased?

Let I be his income
His expenditure is 0.75I
His saving is I-0.75I = 0.25I

His income is increased by 20% => new income is 1.2I
He increases his expenditure by 10% => New expenditure is 1.1 x 0.75I = 0.825I
New saving is 1.2I - 0.825I = 0.375I

His saving increased by (0.375I - 0.25I)/0.25I = 50%

3. Originally Posted by running-gag
Hi

The first one
1. A man spends 75% of his income, when his income is increased by 20%, he increases his expenditure by 10%. By how much per cent are his savings increased?

Let I be his income
His expenditure is 0.75I
His saving is I-0.75I = 0.25I

His income is increased by 20% => new income is 1.2I
He increases his expenditure by 10% => New expenditure is 1.1 x 0.75I = 0.825I
New saving is 1.2I - 0.825I = 0.375I

His saving increased by (0.375I - 0.25I)/0.25I = 50%
Hi
Thanks for replying.....but in the last step, why are u dividing it by 0.25I ?

Can't we say like this:
Old Savings = 0.25I, i.e. 25%
New savings = (1.2-0.825)I = 0.375, i.e. 37.5%
An increase from 25 % to 37.5 % in savings
12.5 %

Am i wrong ?

4. You are wrong because 37.5 is not $\displaystyle 25\cdot 0.125$...

5. For question 3: $\displaystyle \frac {(x-2)^2+(x-1)^2+x^2+(x+1)^2+(x+2)^2}5=66$ $\displaystyle \leftrightarrow \frac {(x^2-4x+4)+(x^2-2x+1)+x^2+(x^2+2x+1)+(x^2+4x+4)}5=66$ $\displaystyle \leftrightarrow \frac {5x^2+10}5=66\leftrightarrow x^2+2=66\leftrightarrow x^2=64\leftrightarrow x=\pm 8$. Therefore the avarage is 8 as well (or if you want: $\displaystyle \frac {6+7+8+9+10}5=8$).

6. Originally Posted by james_bond
You are wrong because 37.5 is not $\displaystyle 25\cdot 0.125$...

Sorry, what does that mean ?

7. ok...i got it now.