Equalising Units Concept (Unchanged Amount)

Given: 1 Equal Ratio (Before), 1 Unequal Ratio (After), Change Amount

First

Cedric and Damian had an equal number of books.

After Cedric threw away 48 books,

the number of books he had left was 1/5 of the number of books Damian had.

How many books did Damian at the start?

Second

Edward and Faris had some stamps in the ratio 1:1.

After Edward lost 95 stamps,

the number of stamps he had was 3/8 of the number of stamps Faris had.

How many stamps did Edward have at the start?

Third

Gareth and Henry had some stickers in the ratio 1:1.

After Gareth used 64 stickers,

the number of stickers he had left was 5/9 of the number of stickers Henry had.

How many stickers did the both of them have altogether in the beginning?

Fourth

Ian had the same number of Halloween sweets as Jack.

When Ian ate 39 of his,

The ratio of the number of Halloween sweets he had to the number of Halloween sweets Jack had became 2 : 5.

How many Halloween sweets do they have altogether at the end?

Fifth

Ken had the same number of chocolate bars as Leonard.

When Ken ate 56 of his,

The ratio of the number of chocolate bars he had to the number of chocolate bars Leonard had became 4 : 11.

How many chocolate bars does Ken have at the end?

Sixth

Austin and Ben had an equal number of books.

After Austin gave away 20 books to the needy,

the number of books he had left was 1/3 of the number of books Ben had.

How many books did Austin have in the beginning?

Given: 1 Equal Ratio (After), 1 Unequal Ratio (Before), Change Amount

First

Cedric had 1/5 of the number of books that Damian had.

After Cedric threw away 48 books,

the number of books he now has is equal to that of Damian's.

How many books did Damian have at the start?

Second

Edward had 3/8 of the number of stamps Faris had.

After Edward lost 95 stamps,

the ratio of the number of stamps between them became 1:1.

How many stamps did Edward have at the start?

Third

Gareth and Henry had some stickers in the ratio 1:1. 

After Gareth used 64 stickers,

the number of stickers he had left was 5/9 of the number of stickers Henry had.

How many stickers did the both of them have altogether in the beginning?

Fourth

Ian had the same number of Halloween sweets as Jack.

When Ian ate 39 of his,

The ratio of the number of Halloween sweets he had to the number of Halloween sweets Jack had became 2 : 5.

How many Halloween sweets do they have altogether at the end?

Fifth

Ken had the same number of Halloween sweets as Leonard.

When Ken ate 56 of his,

The ratio of the number of Halloween sweets he had to the number of Halloween sweets Leonard had became 4 : 11. How many Halloween sweets does Ken have at the end?

Sixth
Austin had 1/3 the number of books Ben had.

After Austin received 20 books from a donor,

the number of books he now has is the same as Ben's.

How many books did Austin have in the beginning?

Given: 2 Ratios (Before + After), Difference Amount

First

Joseph had 2/5 as much money as Tanya. Tanya had $126 more than Joseph. Joseph spent some of his money on a toy. In the end, he was left with 1/3 as much money as Tanya.
How much did Joseph spend on the toy?

Method 1: Finding Unchanged Amount

Tanya (Before) = 126 × 5/3 = $210
Joseph (Before) = 210 × 2/5 = $84

Tanya (After) = $210
Joseph (After) = 210 × 1/3 = $70

Joseph (change) = 84 - 70 = $14

Method 2 : Equalising Unchanged Units

(Before)
Joseph : Tanya
= 2 : 5
= 6 : 15

(After)
= Joseph : Tanya
= 1 : 3
= 5 : 15

Difference (Before) = 15u - 6u = 9u
9u = $126
1u = 126 ÷ 9 = $14

Joseph (Change) = 6u - 5u
= 1u = $14

Given: 2 Ratios (Before + After), Change Amount

First

Mrs Lim baked thrice as many cakes as Mrs Loh. After Mrs Lim gave away 115 cakes, Mrs Loh had twice as many cakes as her. How many cakes did Mrs Lim have left?

Second

Joe and May collected some phone cards in the ratio 3 : 2. When Joe gave away 42 of his phone cards, the ratio of the number of Joe`s phone cards to May`s phone cards became 1 ; 3. How many phone cards did May collect?

Third

There were 680 members in a computer club. 45% of them were boys. When some more boys joined the club, 60% of the members were boys. How many more boys joined the club?