Lesson 10, Topic 4
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# Increasing or Decreasing a Quantity in a Given ratio

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1. To increase a given quantity by a given ratio, use the ratio as a multiplying factor such that the numerator is greater than the denominator.

2. To decrease a given quantity by a given ratio, use the ratio as a multiplying factor such that the numerator is less than the denominator.

Multiplying Factor = $$\frac{new \; quantity}{old \; quantity}$$

### Example 1

Increase the following quantities in the given ratio:

a. 180 km in the ratio of 3:2
b. ₦500 in the ratio of 7:5

Solution

a. New quantity   = $$\scriptsize 180 \; \times \; \normalsize \frac{3}{2} \scriptsize = 270$$

b. New quantity   = $$\scriptsize ₦500 \; \times \; \normalsize \frac{7}{5} \scriptsize = ₦700$$

### Example 2

Decrease the following quantities in the given ratio

a. 180 km  in the ratio  2:3
b. ₦500  in the ratio 3:5

Solution

a. New quantity =$$\frac{2}{3}\scriptsize \; \times \; 180 km = 120km$$

b. New quantity = $$\frac{3}{5}\scriptsize \; \times \; ₦500 = ₦300$$

Evaluation Questions:

1.

a.    What percentage of 300 kobo is 120 kobo
b.    What percentage of 10m is 200cm?
c.    Express ₦600 as a percentage of ₦2400
d.    Express 50 as a percentage of 150?
e.    What percentage of 200km is 40000m?

2.    Express the following ratios in their lowest forms.

a.    16: 36

b.    $$\frac{3}{5} \scriptsize \: : \: 2$$

c.    $$\scriptsize 0.2 \: : \: \normalsize \frac{1}{2}$$

d.    200: 600

e.    30: 150

f.    6hrs : 1 day

3.    Find the missing numbers in the following equivalent ratios

a.    $$\scriptsize 4\: : \: \square = 6 \: : \: 21$$

b.    $$\scriptsize 2\: : \: \square = 14 \: : \: 35$$

c.    $$\scriptsize 3\: : \: 5 = \square \: : \: 1000$$

d.    $$\scriptsize 12 \: : \: 15 = \square \: : \: 25$$

4.

a.    Share  ₦900  between Mary and Martha in the ratio  4:5 respectively.

b.    Share each of the following in the given ratio

i.    6000m in the ratio  2:3
ii.    ₦450 in the ratio 7:8
iii.    75 oranges in the ratio 2:3

c.    The ratio of the cost price to the selling price of a car is 3:4. If the car costs ₦2,100,000 find the selling price.

5.

a.    Increase  ₦150 in the ratio 5:1
b.    Increase 800kg in the ratio 8:5
c.    Decrease  150 oranges in the ratio 1:5
d.    Decrease 800kg in the ratio 5:8
e.    Work out the multiplying factors which change 750m to 900m

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