RS Aggarwal Class 6 Math Tenth Chapter Ratio, Proportion And Unitary Method Exercise 10A Solution
EXERCISE 10A
(1) Find each of the following ratios in the simplest form:
(i) 24 to 56
Solution: HCF of 24 and 56 is 8.
Hence, the simplest form of 24 : 56 is 3 : 7.
(ii) 84 paise to Rs 3
Solution: Rs 3 =300 paise
HCF of 84 and 300 is 12.
Hence, the simplest form of 84 : 300 is 7 : 25.
(iii) 4 kg to 750 g
Solution: 4 kg = 4000 g
HCF of 4000 and 750 is 250.
Hence, the simplest form of 4000 : 750 is 16 : 3.
(iv) 1.8 kg to 6 kg
Solution: 1.8 kg = 1800 g and 6 kg = 6000 g
HCF of 1800 and 6000 is 600.
Hence, the simplest form of 1800 : 6000 is 3 : 10.
(v) 48 minutes to 1 hour
Solution: 1 hour = 60 minutes
HCF of 48 and 60 is 12.
Hence, the simplest form of 48 : 60 is 4 : 5.
(vi) 2.4 km to 900 m
Solution: 2.4 km = 2400 m
HCF of 2400 and 900 is 300.
Hence, the simplest form of 2400 : 900 is 8 : 3.
(2) Express each of the following ratios in the simplest form:
(i) 36 : 90
Solution: HCF of 36 and 90 is 18.
(ii) 324 : 144
Solution: HCF of 324 and 144 is 36.
(iii) 85 : 561
Solution: HCF of 85 and 561 is 17.
(iv) 480 : 384
Solution: HCF of 480 and 384 96.
(v) 186 : 403
Solution: HCF of 186 and 403 is 31.
(vi) 777 : 1147
Solution: HCF of 777 and 1147 is 37.
(3) Write each of the following ratios in the simplest form:
(i) Rs 6.30 : Rs 16.80
Solution: Rs 6.30 = 630 paise and Rs 16.80 = 1680 paise
HCF of 630 and 1680 is 210.
Hence the simplest form of 630 : 1680 is 3 : 8.
(ii) 3 weeks : 30 days
Solution: 3 weeks = 3 x 7 = 21 days
HCF of 21 and 30 is 3.
Hence, the simplest form of 21 : 30 is 7 : 10.
(iii) 3m 5 cm : 35 cm
Solution: 3 m 5 cm = 305 cm
HCF of 305 and 35 is 5.
Hence, the simplest form of 305 : 35 is 61: 7.
(iv) 48 min : 2 hours 40 min
Solution: 2 hours 40 min = 2 x 60 + 40 = 160 min
HCF of 48 and 160 is 16.
Hence, the simplest form of 48 : 160 is 3 : 10.
(v) 1 L 35 mL : 270 mL
Solution: 1 L 35 mL = 1000 + 35 = 1035 mL
HCF of 1035 and 270 is 45.
Hence, the simplest form of 1035 : 270 is 23 : 6.
(vi) 4 kg : 2 kg 500 g
Solution: 4 kg = 4000 g and 2 kg 500 g = 2500 g
HCF of 4000 and 2500 is 500.
Hence, the simplest form of 4000 : 2500 is 8 : 5.
(4) Mr Sahai’s and his wife are both school teachers and earn Rs 16800 and Rs 10500 per month respectively. Find the ratio of
(i) Mr Sahai’s income to his wife’s income;
Solution: HCF of 16800 and 10500 is 2100.
Hence, the simplest form of 16800 : 10500 is 8 : 5.
(ii) Mrs Sahai’s income to her husband’ income;
Solution: HCF of 10500 and 16800 is 2100.
(iii) Mr Sahai’s income to the total income of the two.
Solution: The total income of the two is (16800+10500) = 27300
HCF of 16800 and 27300 is 2100.
Hence, the simplest form of 16800 : 27300 is 8 : 13.
(5) Rohit earns Rs 15300 and saves Rs 1224 per month. Find the ratio of
(i) his income and savings;
Solution: HCF of 15300 and 1224 is 612.
Hence, the simplest form of 15300 : 1224 is 25 : 2.
(ii) his income and expenditure;
Solution: Here the expenditure is (15300 – 1224) = 14076 rupees
HCF of 15300 and 14076 is 612.
Hence, the simplest form of 15300 : 14076 is 25 : 23.
(iii) his expenditure and savings.
Solution: HCF of 14076 and 1224 is 612.
Hence, the simplest form of 14076 : 1224 is 23 : 2.
(6) The ratio of the number of male and female workers in a textile mill is 5 : 3. If there are 115 male workers, what is the number of female workers in the mill?
Solution: Let the number of female workers is x.
So, the number of female workers in the mill is 69.
(7) The boys and the girls in a school are in the ratio 9 : 5. If the total strength of the school is 448, find the number of girls.
Solution: Let the number of student in the school is x.
So, the number of girls in the school is (32 x 5) = 160.
(8) Divide Rs 1575 between Kamal and Madhu in the ratio 7 : 2.
Solution: Total money = Rs 1575
Sum of ratio terms = (7 + 2) = 9
(9) Divide Rs 3450 among A, B and C in the ratio 3 : 5 : 7.
Solution: Total money = Rs 3450
Sum of ratio terms = (3 + 5 + 7) = 15
(10) Two numbers are in the ratio 11 : 12 and their sum is 460. Find the numbers.
Solution: Let the number is x.
So, the required numbers are (11 x 20)= 220 and (12 x 20) = 240.
(11) A 35-cm line segment is divided into two parts in the ratio 4 : 3. Find the length of each part.
Solution: Let the required number is x.
So, the length of the parts are (4 x 5) = 20 cm and (3 x 5) = 15 cm.
(12) A factory produces electric bulbs. If 1 out of every 10 bulbs is defective and the factory produces 630 bulbs per day, find the number of defective bulbs produced each day.
(13) Find the ratio of the price of a pencil to that of a ball pen if pencils cost Rs 96 per score and ball pens cost Rs 50.40 per dozen.
Solution: Here Rs 96 = 9600 paise. So the cost of 1 pencil is (9600÷20) = 480 paiseAnd Rs 50.40 = 5040 paise. So, the cost of 1 ball pen is (5040÷12) = 420 paiseHCF of 480 and 420 is 60.
So, the required ratio is 8 : 7.
(14) The ratio of the length of a field to its width is 5 : 3. Find its length if the width is 42 metres.
Solution: Let the length of the field is x metres.
So, the length is 70 metres.
(15) The ratio of income to savings of a family is 11 : 2. Find the expenditure if the savings is Rs 1520.
Solution: Let the income of the family is Rs x.
Hence, the income of the family is Rs 8360. So, the expenditure of the family is (8360 – 1520) = 6840 rupees.
(16) The ratio of income to expenditure of a family is 7 : 6. Find the savings if the income is Rs 14000.
Solution: Let the amount of the expenditure of the family is Rs x.
Hence, the expenditure is 12000. So, the savings of the family is (14000 – 12000) = 2000 rupees.
(17) The ratio of zinc and copper in an alloy is 7 : 9. If the weight of copper in the alloy is 11.7 kg, find the weight of zinc in it.
Solution: Let the weight of zinc is x kg.
So, the weight of zinc is 9.1 kg.
(18) A bus covers 128 km in 2 hours and a train covers 240 km in 3 hours. Find the ratio of their speeds.
Solution: In 2 hours the bus covers 128 km
Hence the required ratio is 4 : 5.
(19) From each the given pairs, find which ratio is larger:
(i) (3 : 4) or (9 : 16)
(ii) (5 : 12) or (17 : 30)
(iii) (3 : 7) or (4 : 9)
(iv) (1 : 2) or (13 : 27)
(20) Fill in the place holders:
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