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Let me give an example of a situation where there is a proportion. For example, in a library, when a book is overdued by 5 days, the fine is 50 cents and if the book is overdued by 3 days, the fine is 30 cents. Thus,

                 3 days : 5 days = 30 cents : 50 cents

From this example, we can see that proportion is actually a statement that shows that 2 ratios are equal. Thus,

Proportion is a statement that shows that 2 ratios are equal.

1. A man gets $35 for 5 hours of work. How much will he get if he worked for:                                                                       (a) 7 hours;                                                                            (b) x hours?

(a)  

Amount of money received if the man worked for 7 hours                                                                     = $( x 7)                 <== Increase in Ratio            = $ 49

(b)

Amount of money received if the man worked for x hours                                                                     = $(x)                                                               = $7x          

2. 12 men take 2 hours to make 12 tables. How many more men is needed to make 42 tables in an hour?

12 men take 2 hours to make 12 tables.                    12 men take 1 hour to make 6 tables.                       (12 x 7) men takes 1 hours to make 42 tables.

No. of more men needed = (12 x 7) - 12                                       = 72 more men                

1.  A pile of 35 similar books weighs 75 g.                                (a) How much does 150 such similar books weigh?                      (b) How many such similar books are there if the pile weighs 675 g?

2. 5 pipes can fill up a tank with a capacity of 8500 litres with water in 5 minutes.                                                                 (a) How many pipes are needed to fill up a tank with a capacity of 9520 litres with water in 4 minutes?                                   (b) How many minutes is needed for 49 pipes to fill up a tank with 33 320 litres of water?