When two quantity of same unit are compared or divided, it is called as a ratio. The ratio will give a relationship between the values in terms of the quantity. Suppose Jason has $50 and Mike has $150. Then the ratio of their money can be written as `50/150` = `1/3` `implies` 1: 3. This shows that Mike is having an amount that is 3 times of Jason.
This concept will help in dividing certain values among some body else.
Now let us see few problems of this kind.
Example problems ratios:
Ex 1: The sum of the salaries of two persons A and B for a month is $8625.
Their salaries are in the ratio 25: 44. Find their salaries.
Sol: The total sum is $8625.
Total ratio is 25 + 44 = 69
Therefore The salary for A is` 25/69 xx` 8625 = $3125.
The salary for B is `44/69 xx` 8625 = $5500.
Ex 2: Two numbers are in the ratio 7:17. The first number is 441.
Find the second number.
Sol: Let the total value of the two numbers be x. Total ratio is 7 + 17 = 24.
Given : `7/24 xx` x = 441
`implies` x = 441` xx 24/7` = 1512.
Therefore the second number is `17/24 xx ` 1512 = 1071.
More example problems on ratios:
Ex 3: Two groups A and B are of 850 is strength. They are in the ratio 7:10. If 50 of them added to group A and some more to group B, the new ratio will be 8:13. Find number added to B.
Sol: Given: The total is 850.
Ratio is 7:10
`implies` Total ratio is 7 + 10 = 17.
Therefore A group = `7/17 xx` 850 = 350
B group = `10/17 xx` 850 = 500
Now, also given, the new ratio is `[350+50] /[500 +x]` = `8/13` .
`implies ` 13(400) = 8 (500+x)
Therefore 5200 = 4000+8x
Therefore 8x = 5200 – 4000 = 1200
Therefore x = `1200/8` = 150.
Therefore 150 added to B.
Algebra is widely used in day to day activities watch out for my forthcoming posts on pre algebra tutorials and algebra 2 solver free. I am sure they will be helpful.
No comments:
Post a Comment