Ratio + Before After (ALWAYS)

Here is another question from Kiasuparents on Ratio AGAIN! It seems ratio is really a headache for many students. 

A, B and C shared 360 cards. If A gives 10% of her cards to B and in turn B gives 2/7 of his cards to C, the ratio of A's cards to B's cards to C's cards will be 1:3:4. How many cards did B have at first ?

Solution:

Ratio in the end -> A : B : C = 1 : 3 : 4
Total 8u -> 360
1u -> 45
in the end, A -> 45, B -> 135, C -> 180
B gave 2/7 to C, so left 5units
5u -> 135
1u -> 27
After A gave 10% to B, B has 7u -> 7x27 = 189

For A, left 90%, 90% -> 45, 10% -> 5 (A gave 5 cards to B)

No. of cards B had at first: 189 - 5 = 184

Note:

At first, A had 50, B had 184, C had 126

Another Ratio Question (total unchanged)

Here is another ratio question from Kiasuparents

The cost of a birthday present was shared between Benjamin and Christopher. At first, Benjamin paid 2/3 of what Christopher paid. when Benjamin paid $50 more, he ended up paying 4/5 of what Christopher paid. how much was the cost of the present?

Soultion:

Hi use total unchanged (cost of the present is constant)
First B:C = 2:3 (total 5u)
After B:C = 4:5 (total 9u)

Change total units to 45u
First B:C = 2:3 (x9) --> 18:27
After B:C = 4:5 (x5) --> 20:25

2u --> 50
1u --> 25
Cost of present 45u --> $1125 

Another common question on Ratio and Age

Question:

The ratio of the age of Mdm Huda to her son's age is 5:1 now. In 7 years time, she would be thrice as old as her son. What is the total age of Mdm Huda and her son now?

Solution:

Before ratio --> H : S = 5 : 1 (difference 4u)
After ratio --> H : S = 3 : 1 (difference 2u)
Age difference between Mdm Huda and her son is unchanged after 7 years

So make the difference same
After ratio (x2) --> H : S = 6 : 2 (difference 4u now, same as before)
1u (6u-5u) --> 7 years
Age of Mdm Huda now is 5u --> 5x7=35
Age of her son now is 1u --> 7

Units and parts

Question:

Class 5A and 5B have the same number of pupils. The ratio of the number of boys in 5A to the number of boys in 5B is 2 : 3. The number of girls in 5A to the number of girls in 5B is 7 : 4. 
(A) Find the ratio of the number of boys to the number of girls in 5A.
(B) If there are 15 fewer girls than boys in 5B, how many pupils are there in 5B?

Solution:

5A boys : 5B boys = 2u : 3u
5A girls : 5B girls = 7p : 4p

5A and 5B same no. of pupils --> 2u + 7p = 3u + 4p --> 1u = 3p
5A boys : 5B boys = 2u : 3u = 6p : 9p

(A) 5A boys : 5A girls = 6 : 7

(B) 5B boys : 5B girls = 9 : 4 
5parts --> 15 
1p --> 3
No. of pupils in 5B is 13p --> 13 x 3 = 39

Cross Method for Fraction / Ratio Questions

Here is a question from visitor Belnanna:

There were 3/5 as many children as adults on a bus. At the next stop, 3 children boarded and 2 adults alighted from the bus.Then, there were 5/6 as many children as adults on the bus. How many children were there on the bus at first.

Solution:

Ratio, Ratio and Ratio!!

A very common Ration question!

Solution: