# Ratio and Proportion

• Dec 4th 2009, 09:36 PM
saberteeth
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? • Dec 5th 2009, 06:41 AM Grandad Hello saberteeth Quote: 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 £$\displaystyle 28\;(=7+9+12)$. Of this, A's income is £$\displaystyle 7$ and he saves $\displaystyle \frac14$ of it. So he saves £$\displaystyle \frac74$. He spends $\displaystyle \frac34$ of it; so he spends £$\displaystyle \frac{21}{4}$.

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

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 $\displaystyle \frac{7}{4}:\frac{99}{32}: ...$, and simplify the result. I reckon the final answer is $\displaystyle 56:99:279$.

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

• Dec 5th 2009, 07:02 AM
Wilmer
Quote:

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

I make that 56:99:69
Which one of us grandads is correct? (Itwasntme)

224 288 384
168 189 315
=== === ===
056 099 069
• Dec 5th 2009, 07:25 AM
Hello Wilmer
Quote:

Originally Posted by Wilmer
I make that 56:99:78
Which one of us grandads is correct? (Itwasntme)

.

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

Do you agree?

• Dec 5th 2009, 07:35 AM
Wilmer
Yes, this grandad agrees...already edited my typo (AHEM!) (Wondering)
• Dec 6th 2009, 08:16 PM
saberteeth
Thank you!