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EXAMPLE 4. 12 men can reap afield in 25 days. In how many days can 20 men reap the in 30 months?
same field? 10. Forty-five cartons are required to pack 9,000 mathematics books to be sent to a school. If 1,200 more
SOLUTION Clearly, less men will take more days. books are required, how many more cartons will be needed?
And, more men will take less days. 11. The scale of a map is 1 :30,00,000. What is the actual distance between two cities A and B, if they
12 men can reap the field in 25 days, are shown 4 cm apart on the map?
⇒ 1 man can reap the field in (25 ×12) days [less men, more days] 12. If 16 loaves of bread, each weighing 400 g cost ₹200, find the cost of 20 loaves of bread each weighing
(25 12× ) 500g.
⇒ 20 men can reap the field in days [more men, less days)
20 13. If 30 men can weave 450 m of cloth in a day, how many metres of cloth can be woven by 12 men in a day?
= 15 days. EXERCISE 13-D
Hence, 20 men can reap the field in 15 days.
1. Find the ratio of:
EXAMPLE 5 .Find the ratio of price of coffee to that of tea when coffee costs ₹24 per 100 g and a. 25 to 100 b. 60 paise to ₹6 c. 35 minutes to 1 hr
tea costs ₹180 per kilogram. d. 200 ml to 1 L e. 40 cm to 1 metre
2. The number of boys and girls in a school are 2100 and 1800, respec tively. Express the ratio of the
SOLUTION For comparing the price of coffee with that of tea, we have to find the cost of same number of boys to that of girls in the simplest form.
quantity of each of them, say 1 kg. 3. The ratio of milk and chocolate powder in a chocolate cookie is 5:2. Find the weight of each in a
Cost of 100 g of coffee = ₹ 24 chocolate cookie whose weight is 700 grams.
24 4. A sum of ₹10,500 is to be divided between three friends Humpty, Dumpty and Grumpy in the ratio
⇒ cost of 1 g of coffee = ₹ 3:5:7. Find the share of each.
100 5. Ashima’s monthly salary is ₹56,000. She saves ₹8.000 per month. Find the ratio of:
24 (i)her savings to her earnings.
⇒cost of 1000 g of coffee= ₹ × 1000 = ₹ 240
100 (ii)her earning to her expenditure.
⇒ cost of 1 kg of coffee= ₹ 240. (iii)her savings to her expenditure.
Also, cost of 1 kg of tea = ₹ 180. 6. Find the value of x in the following. C. 29:x : : 11 :55
a. 11: 33 : : x:45
b. 85:51 : : x:57
(cost of 1 kg of coffee) : (cost of 1 kg of tea) d. x:124 :: 12:48 e. 18: 14 : : 90:x
= ₹ 240: t 180 7. a. Find the third proportion of the following.
240 240 60 4
÷
= 240:180 = = = = 4:3. (i) 15, 45 (ii) 10, 20 (iii) 14, 42
180 180 60 3 b. Find the mean proportion between the following.
÷
Hence, the required ratio is 4 : 3. (i) 16 and 25 (ii) 25 and 144 (iii) 64 and 81
JUST TRY: 6 The cost of 5 kg of apples is noo. Find the cost of 8 kg of apples. 8. If 2 dozen bananas cost ₹45, find the cost of 5 dozen bananas.
JUST TRY: 7 The cost of 8 pens is t80. What will be the cost of 13 pens? 9. 1 0 labourers can repair a road in 25 days. In how many days will 50 labourers repair it?
JUST TRY: 8 Anita can read 12 pages of a book in 3 minutes. How many pages will she
complete in 2 hours? 10. If 15 litres of petrol is consumed by a car in covering a distance of 250 km, how many kilometres it
will cover with 45 litres of petrol?
EXERCISE 13-C
p
The ratio of a number p to another number q (q ≠ 0) is a fraction and is written as p:q.
1. If 15 litre of petrol is consumed by a car in covering a distance of 250 km, how many kilometers will q
it go with 40 litres of petrol? The ratio of two numbers is expressed in its simplest form.
2. A basket of 25 kg of oranges costs ₹’400. How much will 18 kg of oranges cost? , A ratio has no units.
3. Class VI-A collected ₹3,500 from 50 students for an excursion. In Class VI-B there are 44 students. How A ratio is the comparison between two similar quantities.
much money will the class contribute for the same excursion if the same amount of money is collected from When two ratios are equal, they are said to be in proportion.
each student? If a:b = c:d, then we say that the two ratios are in proportion.
4. Ann earns ₹45,000 in 30 days. How much will be earned in a week? The symbol for proportion is a:b : : c:d.
5. Two dozen eggs cost ₹180. Find the cost of 30 eggs. The first and fourth terms of a proportion are called extremes, the second and third terms are called means.
6. 15 litres of juice can fill 100 small glasses. How many litres of juice will be required to fill 350 glasses? If a, b, c, d are in proportion, then a:b : : c:d
7. Rita brought 15 stamps for ₹250 from the post office. How many stamps can she , buy for ₹470?
8. Jagat pays ₹9.600 as rent for a quarter of a year. What will the rent be for a year? or a:b = c:d
9. A factory produces jute bags. In one year it can produce 2,700 bags. How many bags can it produce or a = c
b d
