the no. of students in a class is 45 , out of which 40% are boys are the rest are girls. the average 3 score in mathematics of the boys is 16*2/3 more than that of girls. if tha average score of all the students is 96 then the average score of the girls
Answers
Answer:
Lets break it down!
Take a deep, slow breath; it’s easier than it looks.
Like you, i’d like to avoid fractions, decimals and irrational numbers if at all possible. They’re so messy —and intimidating.
First things first: since the class size is 40, and there’s 45% boys —55% will be girls. Since we *know* 50% is exactly half … and half of 40 (class size) is 20, it follows there’s slightly less than 20 boys and slightly more than 20 girls.
Now the fun part. The question gives a couple of gifts that yield us some juicy whole numbers if we know where to look:
The question deals with multiples of 5% (45% boys) — great! That’s because 5% is the equivalent of 1/20! Remember the class size is 40: a multiple of 20!
Now, the rest of the problem is real easy to solve. Let’s do it! We’ve now got the whole numbers we need.
5% of 40 is 40/20. That’s 2. This is key. Essentially all we’re doing from now on is multiplying our key number, 2
Remember 45% is 9 times 5%. 5% of 40 is 2, 9 times 2 is 18. So, there’s 18 boys in the class. 18 is a little less than 20, so that seems to fit. 18 boys.
We can then deduct the 18 boys from the 40 children and get 22. That’s 22 girls! 22 is a bit over 20, so it looks right and we can leave it there.
Want further proof? OK. Earlier we deduced that we have 55% girls. That’s 11 times 5%. That’s 11 times 2 = 22. 22 girls.
Just to make sure: 18 plus 22 is 40.
Yet another angle:
45% is 5% less than 50%. That means 2 less than 20, which 18.
55% is 5% more than 50%, that means 2 more than 20. That’s 22!
Now we know for sure: 18 boys, 22 girls.
Some handy shortcuts:
•Break it down if you can!
• Remember your basic times tables. This saves you from reinventing the wheel every … dang … time …
• 50% (or 50/100) is exactly half; 5% is any given amount is that number/20; 10% is 1/10 of any given no. If the numbers in your problem are —or turn out to be— multiples of 2, 5, ten … you have an *easy* problem to solve, especially if you know your basic times tables ^_~