hi Phoenix,

Q1 Daniel had some stamps. 40% of them are local and the rest are foreign stamps. He gave away 20% of the local stamps and 1/3 of the foreign stamps. What % of the stamps was left?

Soln:

At First: 5u of stamps in total, as

Local stamps: 2u

Foreign stamps: 3u

Gave away: 0.2 x 2u = 0.4u local, + 1u foreign = 1.4u total given away

thus, left with 5u - 1.4u = 3.6u stamps, i.e, 3.6u / 5u x 100% = 72%

Q2 A class was fixing a puzzle of their photos.In the first hour, the ratio of the number of fixed pieces to unfixed pieces is 1:5. In the next hour, they fixed another 15 pieces of the puzzle. Finally, the number of fixed pieces became 60% of the unfixed pieces. How many pieces were there in the puzzle?

Soln:

.....................fixed........unfixed

1st hour: ....... 1u.............5u

2nd hr: ........+ 15...........- 15

finally:........... 3p.............5p

thus, ........... 1u + 15 = 3p

so that, (x5): 5u + 75 = 15p

and, ............ 5u - 15 = 5p

therefore, 10p = 90

and so, .....1p = 9

that is to say, there were 8p = 8 x 9 = 72 pieces in the puzzle.

Check: 3p - 15 = 3 x 9 - 15 = 12 (no. of fixed in 1st hr), vs. 5p + 15 = 5 x 9 + 15 = 60 (unfixed pcs in 1st hr)

giving a ratio of fixed to unfixed in 1st hr as 12 : 60 = 1: 5

Q3 Jude had 20% more money than Ken. Jude gave 40% of his money to Ken. Ken than gave 50% of his money to Jude. In the end, Ken had $216 less than Jude. How much did Jude have at first?

Soln:

.........................Jude.................Ken

at 1st:...............120%...............100%

Jude gave:..... - 48%..............+ 48% .................[40% of 120% = 0.4 x 120% = 48%]

so:.................... 72%................148%

Ken gave:.......+ 74%...............- 74%

in end:.............146%.................74%

that is, 146% - 74% = 72% -----> $216

therefore, 120% ------> $216 / 72 x 120 = $360, and this is what Jude had at first

Q4. The number of pupils in the hall is twice the number of pupils in the canteen. 3/4 of the pupils in the hall were boys and 3/5 of the pupils in the canteen were girls. If there were 6 more girls in the canteen than in the hall, find the number of pupils in the hall.

Soln:

...................................hall.......................................canteen

no. pupils:..................10u............................................5u

made of:.........7.5u boys + 2.5u girls.................2u boys + 3u girls

so that, 3u - 2.5u = 0.5u ---------> 6

thus, ........................1u --------> 12

And so, there are 10u = 120 pupils in the hall.

Q5. Mrs Lim bought some bowls and plates. If she buys another 5 bowls, there are 60% as many bowls and [should be, as?] plates.

......................................................................................................................................................................^^^^^^^^^^^^^^^

If she buys another 9 plates, there will be thrice as many plates as bowls. How many bowls did she buy?

Soln:

....................................bowls.................plates

......................................1p.......................5u

Scenario 1:...................+ 5

..............................so, 3u = 1p + 5

............................and, 1u = (1/3)p + (5/3)

............................thus, 5u = (5/3)p + (25/3)

Scenario 2: .............................................+ 9

...........................then, 5u + 9 = 3p

..............................so, (5/3)p + (25/3) + 9 = 3p

................................(4/3)p = 52/3

...................that is, 1p = 52 / 4 = 13

therefore, Mrs Lim bought 13 bowls.

Check: and she bought 5u = (5/3) x 13 + 25/3 = 30 plates.

then, scenario 1: 13 + 5 = 18 = 60% of 30

and, scenario 2: 30 + 9 = 39 = 3 times 13

Hope all these help. Enjoy!