More complex Ratio

Note: In the following questions, / will be substituted for the division sign.Answers in BOLD
Ratio, as i have said before,can be manipulated to suit many questions.Now, i shall introduce to you some methods you might consider using when doing problem sums.
Some basic questions.
1. 16/23 of a class of pupils are girls.What is the ratio of the number of girls to the number of boys?
Ans:16:7


2. The ratio of A's stamps to B's stamps is 8:11.If A gives 9 stamps to B, both of them will have an equal amount of stamps. How many stamps does B have?
Ans + formula:
8 units + 11 units = 19 units (total stamps of A and B)
19 units / 2 = 9.5 units (in the end when they have the same amount of stamps.)
9.5 units - 8 units = 1.5 units (difference between at first and in the end)
1.5 units --> 9
0.5 units --> 3
1 unit --> 6
B has 6 x 11 = 66 stamps.


3. A is 1:3 the total of the number of sweets.The ratio of sweets for B is to C is 5:2.Find the ratio of A:B:C.
Ans + formula:
A:A+B+C B:C
1:3 5:2
B+C=7 units= 2/3 of total sweets.
Let us make this easier to do. B:C=5:2=10:4 B+C=14 units=2/3 of sweets
Total number of sweets=21 sweets. A=7 sweets B= 10 sweets C= 4 sweets
Thus,the answer is 7:10:4

Common mistakes:
Do take note that if you use the initial ratio of B:C=5:2, your answer would be incorrect.

4.Shanti will be 13 years old next year.The ratio of Shanti's age to Michael's age is 2:3 now.Find the ratio of Shanti"s age to Michael"s age 5 years ago.
Ans + formula:
Shanti = 12 years old (present)
2 units = 12 years old
3 units = 18 years old = Michael"s present age
Michael"s age 5 years ago= 18-5=13
Shanti"s age 5 years ago= 12-5=7
Ans:7:13
Common mistakes:
A few people may have read the first sentence wrongly and intepreted that Shanti was 13 this year.If they have,they would find a wrong answer.Always remember to read your question carefully.

5.The ratio of apples to pineapples in a basket was 4:5. After 290 apples and pineapples were added into the basket,there were twice as many apples and thrice as many pineapples as before.What was the total number of fruits in the basket at first?
Ans + formula:
4:5 -------------->8:15
+ 280 each
Difference made by the addition of 280=8u-4u 15u-5u=10u 10u+4u=14u
280/14=20
1 unit =20
9 units =180

6.James and Ming had the same amount of money.After James spent $120 and Ming spent 1:4 of his money,the ratio of James"s money to Ming"s money was 1:2.How much money was James left with?
Ans + formula:
J:M(shortform for James and Ming)=1:2=3:6
6 units=3:4 of Ming"s original amount of money.
Ming spent=2 units
8:8 at first ------>3:6
$120= 8 units - 3 units = 5 units
1 unit = $24
3 units= $72

7.Last year,the ratio of the number of boys to the number of girls in the Chess club was 5:3.This year,20 members joined the club.The new ratio was then 3:2.There are 36 boys in the club now.How many of the 20 new members that joined this year are girls?
Ans + formula:
3 units =36 1 unit =12 2 units = 24
36 boys and 24 girls this year.
Total members=24+36=60
Original members=60-20=40
8 units = 40 members
Boys = 5 units=25 Girls=3 units =15
15+?=24
Increase in girl members=15+9=24
Common mistakes:Students are confused between the two ratios.Students should label the first ratio as "last year" and the second ratio as "this year".

8.The ratio of the number of chairs to the number of tables in a shop was 3:1.After selling 53 chairs and 7 tables,the ratio of the number of chairs to tables left became 1:3.How many tables were there in the shop at first?
Ans + formula:
C:T(shortform for chairs to tables)= 3 u:1 u------->x:3 x
sell 53 C and 7 T
1 u-7=3x___________________________________
3 u-53=x
3(3 u -53=x)=9 u-159=3x which also means that 9 u-159 = 1 u-7
Therefor,I can cancel out the u and it will become
8u-159 =-7 which also means that 159-7 = 8 u
8 u=152
1 u=19
Note: Some may feel uncomfortable using algebra and ratio together.You should try coming up with your own solutions.