Math Help - Ratio and Proportion

1. Ratio and Proportion

1) The income of A,B and C are in the ratio of 7:9:12 and their spending are in the ratio of 8:9:15. If A saves 1/4th of his income, then the savings of A, B,C are in the ratio of?

2) A diamond falls down and breaks into three pieces whose weights are in the ratio 2:3:5. The value of diamond is proportionate to the square of it's weight. If the value of the original diamond is $20,000, what is the loss in value due to breakage? How do i solve these? 2. Hello saberteeth Originally Posted by saberteeth 1) The income of A,B and C are in the ratio of 7:9:12 and their spending are in the ratio of 8:9:15. If A saves 1/4th of his income, then the savings of A, B,C are in the ratio of? 2) A diamond falls down and breaks into three pieces whose weights are in the ratio 2:3:5. The value of diamond is proportionate to the square of it's weight. If the value of the original diamond is$20,000, what is the loss in value due to breakage?

How do i solve these?
1) Consider a total income of £ $28\;(=7+9+12)$. Of this, A's income is £ $7$ and he saves $\frac14$ of it. So he saves £ $\frac74$. He spends $\frac34$ of it; so he spends £ $\frac{21}{4}$.

B's income is £ $9$, and his spend is $\frac98$ of A's spend. So he spends £ $\frac98\times\frac{21}{4}=$ £ $\frac{189}{32}$. Therefore he saves £ $\left(9-\frac{189}{32}\right) =$ £ $\frac{99}{32}$.

I'll leave you to work out C's spend and saving in the same way.

When you've done that, write the savings as a ratio $\frac{7}{4}:\frac{99}{32}: ...$, and simplify the result. I reckon the final answer is $56:99:279$.

2) $2 + 3 + 5 = 10$. So the weight of the smallest piece is $\frac{2}{10}=0.2$ of the weight of the original single diamond. So its value is the square of this fraction multiplied by the original value, which is:
$$0.2^2 \times 20,000 =$$ $800$
Work out the value of the other two pieces in the same way. Add these values together, and subtract from $$20,000$ to find the total loss in value. I reckon the answer is$ $12,400$.

Grandad

3. Originally Posted by Grandad
When you've done that, write the savings as a ratio $\frac{7}{4}:\frac{99}{32}: ...$, and simplify the result.
I reckon the final answer is $56:99:279$.

Grandad
I make that 56:99:69
Which one of us grandads is correct?

224 288 384
168 189 315
=== === ===
056 099 069

4. Hello Wilmer
Originally Posted by Wilmer
I make that 56:99:78
Which one of us grandads is correct?

.
I've just done it again, and got $56:99:69$. So, if that's right, then neither of us was correct! (In my first attempt I dropped a digit and worked out $5\times21$ instead of $15\times 21$.)

Do you agree?

Grandad

5. Yes, this grandad agrees...already edited my typo (AHEM!)

6. Thank you!