Given: Original (Before), Remainder (After) Ratios
Find: Original (Before) Amount
First
Raymond spent 25% of his money on a toy car.
He spent 0.4 of the remaining amount on a box of batteries.
a) What percentage of his money was left?
b) If Raymond spent $12 on the box of batteries, how much did he have at first?
(Original)
Toy Car : Remainder : Original
= 25 : 75 : 100
= 1 : 3 : 4
= 5 : 15 : 20
(Remainder)
Batteries : Left : Remainder
= 0.4 : 0.6 : 1.0
= 2 : 3 : 5
= 6 : 9 : 15
Left = 9/20 × 100% = 45%
Batteries = 6u = $12
Original = 20u = $40
Second
Mrs Jacob spent 1/6 of her salary on a washing machine and 2/3 of the remainder on a television set.
If she saved the remaining $750, how much was her salary?
Third
Mrs Lim baked a certain number of egg tarts.
She gave 1/8 of the tarts to her neighbour and 1/4 of the remainder to her cousin.
She was left with 42 tarts.
How many tarts did she bake at first?
Fourth
Benedict spent 2/9 of his pocket money on books, 2/5 of the remainder on magazines and saved the rest.
a) What fraction of his money did Benedict save?
b) If he spent $16 more on the magazines than on books, how much did he have at first?
Fifth
James had a number of coloured balls in his ball pit. 1/4 of the balls were red, 2/3 of the remaining balls were blue and the rest were green. Given that there were 120 red and green balls altogether, how many balls were there in the ball pit?
Sixth
At a book fair, 2/5 of the customers were men. There were thrice as many women as children. If there were 95 more men than children, how many customers were there at the book fair?
Seventh
During an entrepreneur competition, a team of pupils spent 3/7 of their capital on raw materials, 1/2 of the remaining capital on publicity and $80 on stall setup. If they were left with $40, find the amount of their capital at first.
Eighth
At a school carnival, 40% of the people are men and the rest are women and children in the ratio of 4 : 5. If there are 145 more men than children at the carnival, how many people are there at the carnival altogether?
Ninth
In a class, 40% of the pupils like badminton. The rest of the pupils prefer table tennis and basketball in the ratio 1 : 2. Given that 8 more pupils prefer badminton to table tennis, how many pupils are there in the class?
Tenth
Junhua spent 2/9 of his salary on food and gave 4/7 of the remainder to his father.
Then he saved the rest. If his father received $400 from him, how much was Junhua's salary?
Given:
2nd Item: Remainder Ratio
Left : Original Ratio
First
Mellie spent $120 on a dress.
Then she spent 2/5 of her remaining amount of money on a wallet.
Given that she had 1/3 of her original sum of money left, how much money did she have at first?
Ratio Method (Equalise 'Left' Units)
(Remainder)
Wallet : Left : Remainder
= 2 : 3 : 5
(Original)
Left : Original
= 1 : 3
= 3 : 9
Dress = Original - Remainder = 9u - 5u
= 4u = $120
Original = $120 ÷ 4 × 9 = $270
Common Numerator Method
(Left)
1 - 2/5 = 3/5 of Remainder
1/3 of Original = 3/9 of Original
Dress = Original - Remainder
= 9u - 5u = 4u
4u = $120
Original = 9u
9u = 120 ÷ 4 × 9 = $270
Fractions + Working Backwards Method
(Left)
1 - 2/5 = 3/5
(Original)
3/5 × 3 = 9/5
Remainder = 5u
Original = 9u
Dress = 9u - 5u = 4u
4u = $120
9u = 120 ÷ 4 × 9 = $270
Second
Mr Tan spent $1280 of his salary on a television set and 1/3 of the remainder on a DVD player.
If he had 2/5 of his salary left, how much was his salary?
Ratio Method
(Remainder)
DVD : Left : Remainder
= 1 : 2 : 3
(Original)
Left : Original
= 2 : 5
TV = Original - Remainder = 5 units - 3 units
= 2 units = $1280
Salary = 5 units = $3200
Third
Mrs Amos spent $2500 of her salary on a pair of diamond earrings 20% of her remaining salary on a leather bag. She had 0.4 of her salary left.
a) How much was Mrs Amos' salary?
b) How much did the leather bag cost?
Fourth
Mr Edward spent $1200 of his salary on a sound system. He gave 2/3 of the remainder to his wife and save the rest. If he saved 1/4 of his salary, how much was his salary?
Fifth
In a class, 16 of the pupils are boys. Then 3/4 of the girls left the classroom. If 1/6 of the original number of pupils are now girls, find the number of pupils in the class at first.
Sixth
In a class, 12 pupils are in the band and 3/4 of the remaining pupils are in the Modern Dance club.
If 1/5 of the class are in neither the band nor the club, how many pupils are there in the class?
Seventh
Mrs Ng went to a shopping centre and spent $120 on a wallet. She then used 2/3 of the remaining amount of money to buy a dress. She was left with 1/5 of her original amount of money. How much did she have at first?
Eighth
Miss Rita bought a certain number of chocolate for her pupils.
She gave 84 chocolates to class 6A and 2/5 of the remainder to class 6B.
If she was left with 1/4 of the original number of chocolates, how many chocolates did she have at first?
Ninth
Mr Tho spent $1220 of his savings on a television set and 2/5 of the remainder on a hi-fi set.
He had 1/3 of his origin amount of savings left.
a) Find Mr Tho's original amount of savings
b) Find the cost of the hi-fi set
Tenth
At a funfair, there were 250. 3/7 of the rest of the people were women. Given than 1/2 of the people at the funfair were children, how many women were there?
Eleventh
Mr Krishnan had a sum of money. He gave $1400 to his wife and spent $400 on a washing machine. He then gave 2/5 of the remainder to his 3 children. Given that each child received 1/12 of Mr Krishnan's original sum of money, how much did each child receive?
Twelfth
Mr Edward spent $120 in one shop and 40% of the remainder in another shop. He had 30% of his original amount of money left after shopping. Find the amount of money he had at first.
During a travel fair, 90 families chose Hong Kong as their travel destination. 80% of the remaining families chose Taiwan while the rest chose Malaysia. Given that 1/10 of the families chose Malaysia, how many families were there at the travel fair?
Mr Jones spent $990 on a DVD player and 55% of the remainder on a sofa set. He was left with 30% of his original amount of money. Find the amount of money he had at first.
During a travel fair, 90 families chose Hong Kong as their travel destination. 80% of the remaining families chose Taiwan while the rest chose Malaysia. Given that 1/10 of the families chose Malaysia, how many families were there at the travel fair?
Mr Jones spent $990 on a DVD player and 55% of the remainder on a sofa set. He was left with 30% of his original amount of money. Find the amount of money he had at first.
KIV
1/2 of the pupils in a school were girls and the rest were boys. 2/5 of the girls and 2/3 of the boys took part in a school charity event. Find the total number of pupils in the school if 280 pupils did not take part.
At a funfair, there were twice as many males as females. 3/4 of the males were boys and the rest were men. 1/2 of the females were women and the rest were girls. Given that there were 120 more boys than girls, how many adults were at the funfair altogether?
At a trade fair held at Singapore Expo, the ratio of the number of males to the number of females who attended the trade fair was 3 : 2. There were twice as many men as boys and 2/3 of the females were girls. Given that there were 90 more girls than boys at the trade fair, find the total number of people at the trade fair.
At a trade fair held at Singapore Expo, the ratio of the number of males to the number of females who attended the trade fair was 3 : 2. There were twice as many men as boys and 2/3 of the females were girls. Given that there were 90 more girls than boys at the trade fair, find the total number of people at the trade fair.
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