1Find the ratio in each of these pairs: (a) 4 hrs and 6 hrs (b) 12 ft and 9 ft (c) 250 gram and 2 kg (d) 3 kg and 850 gram (e) 2 hrs and 45 minutes (f) 40 minutes and 1 hr (g) 2 l and 850 ml (h) Rs 5 and 90 paisa
2(a) In one school the ratio of boys to girls is 5:8. If there are 480 girls, how many boys are there? (b) In another school the ratio of teachers to students is 1:32. If the school has 25 teachers, how many students are there? (c) In a third school the ratio of boys to girls is 3:5. If there are 330 boys, how many girls are there?
3(a) Rs 840 is shared between John and Joseph in the ratio 3:4. How much does each of them get? (b) Two shopkeepers together bought 50 dozen exercise books of the same kind. They shared them in the ratio 5:7. How many did each shopkeeper get?
4(a) On a map drawn to a scale of 1:2000, two places are 8 cm apart. What is the real distance between them? (b) On a map drawn to a scale of 1:4000, two places are 5 cm apart. What is the real distance between them?
5(a) The present ages of Rita and Narma are in the ratio 4:5. Two years ago the ratio of their ages was 3:4. Find their present ages. (b) Two brothers spent money on a friend's birthday in the ratio 4:5. If each of them had spent Rs 10 more, the ratio of their spending would have been 5:6. How much did each spend? (c) Two numbers are in the ratio 1:3. When 5 is added to both, they are in the ratio 1:2. Find the numbers. (d) The present ages of Ali and Amir are in the ratio 3:4. Three years ago the ratio of their ages was 2:3. Find their present ages.
6(a) Rs 216 is shared among three girls aged 8, 9 and 10 in the ratio of their ages. How much does each girl get? (b) Bipin, Amrit and Ashish ran a business with investments in the ratio 2:5:6. After a year they earned Rs 65,00,000. How much did each of them earn?
7(a) B saves twice as much as A, and C saves three times as much as B. Their savings come to Rs 98460 in all. How much did each save? (b) Krishna saves twice as much as Ram, and Hari saves three times as much as Krishna. Their savings come to Rs 16200 in all. How much did each save?
8(a) The angles of a triangle are in the ratio 1:1:2. Find the angles. (b) The angles of a triangle are in the ratio 2:3:4. Find the angles.
9Check whether each of these sets of numbers is in proportion: (a) 5, 8, 10, 15 (b) 3, 5, 6, 10 (c) 1 kg, 4 kg, 6 kg, 10 kg (d) 5 cm, 8 cm, 10 cm, 16 cm (e) 5 m, 3 m, 25 m, 15 m (f) 3 ft, 8 ft, 12 ft, 22 ft
10Each of these sets is in proportion. Find the missing term: (a) a, 3, 3, 9 (b) 3, x, 6, 8 (c) 2, 5, 8, d (d) x, 2, 6, 4 (e) 16, 4, 4, y (f) 7, 9, z, 18
11Find the value of x: (a) x:5 = 10:25 (b) 3:7 = 21:x (c) 10:x = 2:11 (d) 25:15 = x:3
12(a) What number added to both 12 and 21 makes their ratio 5:8? (b) What number added to both 15 and 25 makes their ratio 2:3? (c) What number subtracted from both 24 and 30 makes their ratio 3:4?
13(a) If Rs 600 buys 12 exercise books, how many will Rs 900 buy? (b) If Rs 50 buys 5 pens, how many will Rs 240 buy?
14(a) In a school the ratio of students who use pencils to students who use pens is 10:11. If 110 students use pencils, how many use pens? (b) The ratio of students who eat lunch at school to those who bring lunch from home is 3:2. If 321 eat at school, how many bring lunch from home? (c) Rina and Mina are sisters. The money they spent on books is in the ratio 3:2. If Mina paid Rs 824, how much did Rina pay? (d) A sweet is made with milk and sugar in the ratio 5:2. If it contains 750 gm of milk, how much sugar does it contain? (e) The gravity of the moon and of the earth are in the ratio 1:6. An object weighs 90 N on the earth. What does it weigh on the moon?
15(a) Kopila's marks in four subjects are in proportion. If the marks are 25, 30, 75 and x, find the value of x. (b) The money Abdul spent on snacks over four months is in proportion. If the amounts are 150, 200, x and 240, find the value of x.
16Note down the ages of the members of five families in your neighbourhood. Sort them into three groups, up to 16 years, 17 to 40 years, and above 40 years, and present the sizes of the three groups as a ratio.
17In a class the ratio of boys to girls is 7:5 and there are 60 students in all. How many boys and how many girls are there? Also write the ratio of the number of girls to the total number of students.
18Ramesh says, "I bought 2 kg of potatoes and 500 gm of onions, so the ratio of potatoes to onions is 2:500." Where has Ramesh gone wrong? Write the correct ratio.
19Four numbers 6, 9, 10 and 15 are given. Check whether they are in proportion, and in your working name which numbers are the Extremes and which are the Means.