1) The number of boys was 2⁄3 the number of girls at a birthday party. Later, 12 more boys joined and 6 girls left the party. In the end, there were twice as many boys as girls at the party. Find the number of boys at the party at first.
Ans :- At first there were 12 boys at the party.
2) Joash, Tobias and Hansen shared a box of marbles. The number of marbles Joash took was 8 more than 1⁄3 of the marbles in the box. The number of marbles Tobias took was 18 more than ½ of the remaining marbles. Hansen took the last 6 marbles that were left. How many marbles were there in the box?
Ans :- There were 84 marbles in the box.
3) Weiming had 2⁄3 as many stickers as Shiyang. After Weiming gave 52 stickers to Shiyang, Weiming had 2⁄5 as many stickers as Shiyang. How many stickers did Weiming have at first?
Ans :- At first Weiming had 182 stickers.
4) Both Joanne and Joseph had an equal amount of money at first. Every month, Joanne spent $850 and Joseph spent $912. After a few months, Joanne was left with $1550 while Joseph had 4⁄5 as much as Joanne. How much money did Joseph have at first?
Ans :- At first Joseph had $5800
5) Mr Wu had some badges and decided to give them to his two sons, Sean and Matthew. Mr Wu gave 1⁄3 of the badges and 8 more badges to Sean. He gave 3⁄4 of the remainder to Matthew but took back 2 badges. Mr Wu was left with 26 badges. How many badges did Mr Wu have at first?
Ans :- At first Mr Wu had 156 badges.
6) A flask is 1⁄3 filled with chocolate powder. A teapot is twice as large as the flask and is ¼ filled with chocolate powder. Then the flask and the teapot are each filled with water completely and all the contents are mixed together into a chocolate drink. What fraction of the chocolate drink is chocolate powder?
Ans :- 5⁄18 is chocolate powder.
7) Alexa received a number of text messages on her mobile phone. 2⁄11 of them were from her superiors. 3⁄5 were from her parents and 1⁄6 of the remaining text messages were from her cousins. There were a total of 559 text messages from her superiors and her parents. How many text messages were from her cousins?
Ans :- 26 Text messages were from Alexa's cousin.
8) The cost of a packet of dried prunes was 1⁄7 that of a packet of dried mangoes. A shopkeeper spent 4⁄9 of his money on 24 packets of dried mangoes and 24 packets of dried prunes. Then he used the rest of his money to buy another 9 packets of dried mangoes and some more dried prunes.
(a) If he had spent all 4⁄9 of his money on dried prunes, how many packets of dried prunes could he buy?
(b) How many packets of dried prunes did he actually buy altogether?
Ans :- a) He could buy 192 packets of dried prunes.
b) Altogether he actually bought 201 packets of dried prunes.
9) At a rugby match, ¼ of the spectators bought 1 pack of titbits each. 3⁄5 of the remainder spectators bought 2 packs of titbits each. The rest of the spectators bought 4 packs of titbits each. Given that all the spectators bought 3854 packs of titbits, how many spectators were there at the match?
Ans :- There were 1640 spectator at the match.
10) There were 32 tourists on a bus. 2⁄5 of the men and ¼ of the women were from Singapore. The total number of tourists who came from Singapore was 11. How many men came from Singapore?
Ans :- 8 men came from Singapore.