What is Proportion:
The mathematical comparison between two numbers is called Proportion
Proportions are of two kinds:
(i) Direct proportion
(ii) Inverse proportion
(I) Direct proportion: The relationship between two quantities in which an increase or decrease in one quantity causes a proportional increase or decrease in the second quantity respectively is called direct proportion.
(ii) Inverse proportion: The relationship between two ratios in which an increase in one quantity causes a proportional decrease in the second quantity and vice versa is called an inverse proportion.
Compound Proportion:
The relationship between two or more simple ratios (proportions) is called Compound proportion.
or
We can say that the proportion involving two or more quantities is called Compound proportion.
Let a:b and c:d are the two ratios among four quantities a, b, c, and d. Mathematically the relationship between these two ratios can be written as a : b : : c : d.
Word Problem No. 1:
30 men repair a road in 56 days by working 6 hours daily. In how many days 45 men will repair the same road by working 7 hours daily? (Ans. 32 days)
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Word Problem No. 2:
If 60 women spin 48 kg of cotton by working 8 hours daily, how much cotton will 30 women spin by working 12 hours daily? (Ans. 36 kg)
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Word Problem No. 3:
If the price of a carpet 8 metres long and 3 metres wide is Rs. 6288, what will be the price of 12 metres long and 6 metre wide carpet? (Ans. 18,864 Rs.)
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Word Problem No. 4:
If 15 laboures earn Rs. 67,500 in 9 days, how much money will 10 laboures earn in 12 days? (Ans. 72,000 Rs.)
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Word Problem No. 5:
70 men can complete a wall of 150 metres length in 12 days. How many men will complete the wall of length 600 metres in 30 days? (Ans. 112 men)
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Word Problem No. 6:
If the fare of 12 quintal luggage for a distance of 18 km is 12 rupees, how much fare will be charged for a luggage of 9 quintals for a distance of 20 km? (Ans. 10 Rs.)
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Word Problem No. 7:
14 masons can build a wall 12 metres high in 12 days. How many masons will be needed to build a wall 120 metres high in 7 days? (Ans. 240 masons)
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Word Problem No. 8:
15 machines prepare 360 sweaters in 6 days. 3 machines get out of order. How many sweaters can be prepared in 10 days by the remaining machines? (Ans. 480 Sweaters)
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Word Problem No. 9:
1440 men had sufficient food for 32 days in a camp. How many men may leave the camp so that the same food is sufficient for 40 days when the ration is increased by 1`\frac{1}{2}` times? [Hint: The 1st element (food) is 1 and the 2nd element (food) is `\frac{3}{2}` ] (Ans. 768 Men)
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Word Problem No. 10:
Ten men can assemble 400 cycles in 8 days. How many cycles 5 men will assemble if they work for 16 days? (Ans. 400 Cycles.)
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Word Problem No. 11:
If the price of 12 Eggs is Rs.96, how many eggs can be bought with Rs.80? (Ans. 10 eggs)
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Word Problem No. 12:
10 men have ration for 21 days in a camp. If 3 men leave the camp, for how many days will the ration be sufficient for the remaining men? (Ans. 30 days)
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Word Problem No. 13:
If 35 labourers dig 805 cm³ of earth in 5 hours, how much of the earth will 30 labourers dig in 6 hours? (Ans. 828 cm³)
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Word Problem No. 14:
Rs.8,000 are sufficient for a family of 4 members for 40 days. For how many days Rs.15,000 will be sufficient for a family of 5 members? (Ans. 60 days)
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Word Problem No. 15:
If 4200 men have sufficient food for 32 days at a rate of 12 hectogram per person, how many men may leave so that the same food be sufficient for 42 days at a rate of 16 hectogram per person? (Ans. 2,400 Men)
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1. Real Life Word Problems on Financial Mathematics, Property Tax, General Sale Tax (GST), Zakat, Ushr, Profit and Loss, Markup, Percentage, Proportion.
2. 5th class Notes: English, Social Study (S.St.), General Science (G.Sc.), Urdu (اُردو), Islamiat (اسلامیات), Mathematics
3. 6th class Notes: Mathematics
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