NCERT 6TH CLASS MATHS RATIO & PROPPRTION PART- lll
ANSWER KEY - Multiple Choice questions: 1. (a) 5 times Hint: 10 = 5 × 2 2. (a) 2: 3 Hint: 80000 = 2 × 40000 3. (a) 2:3 Hint: 20/30=2/3= 2: 3 4. (a) 1:2 Hint: 25/(25+25 )=25/50 = 12 = 1: 2 5. (b) 5:4 Hint: 150/120 = 15/12 = 5/4 = 5: 4 6. (a) Hint: 50,000/3,00,000 = 1/6 = 1: 6 7. (b) 3:1 Hint: 6/2 = 3/1 = 3: 1 8. (d) 5:4. Hint: 50/40 = 5/4 = 5: 4 9. (a) 2:5 Hint: 1 m = 100 cm 40/100 = 2/5 = 2: 5 10. (a) 1:2 Hint: 4/8 = 1/2 = 1: 2 11. (c) 6: 9 Hint: 2: 3 = 2/3= (2×3)/(3×3) = 6/9= 6: 9 12. (a) 1:2 Hint: 13. (d) 3: 2 Hint: 12: 8 = 12/8= (12÷4)/(8÷4) = 3/2= 3: 2 14. (c) 1: 25 Hint: 20: 500 = 20/500=1/25= 1: 25 15. (b) 5:12 Hint: 1 hour = 60 minutes 25: 60 = 25/60=5/12= 5: 12 Match The Following: Fill in the blanks: 1. If 4, a, a, 36 are in proportion then a is equal to 12. 2. 32 m: 64 m:: 6 Sec: 12 Sec. 3. 5: 4 = 30: 24. 4. If a = 2b then a: b = 2: 1. True /False: 1. True 2. False 3. True 4. False Very Short Answer: 1. X: 6 = 25: 5 2. It is given that Weight of 25 copies = 5 kg ∴ Weight of 1 copy = 5 ÷ 25 = 1/5 kg ∴ Weight of 30 copies = 30 ×1/5= 6 kg 3. 45km: 60km = 45/60 = (45÷15)/(60÷15) [∴ H.C.F.(45, 60) = 15] = 3/4 = 3: 4 12 hours: 15 hours = 12/15=(12÷3)/(15÷3 ) [∴H.C.F.(12, 15) = 3] =4/5=4:5 Since, the two ratios are not equal, therefore the given statement is false(F). 4. 24: 27 = 24/27=(24÷3)/(27÷3) [∴H.C.F.(24, 27) = 3] = 8/9=8:9 8: 9 = 24: 27 ∴ 8: 9:: 24: 27 is true(T). 5. 7.5 liter: 15 liter 6. 7. Let 2A = 3B = 4C = x 8. The given numbers are not in the same units. So, converting them into same units. 1.5 m = 1.5 × 100 cm = 150 cm [∵ 1 m = 100 cm] ∴ The required ratio is 75 cm: 150 cm. ∴ Required ratio = 1: 2 9. Thus, 9: 15 and 6: 10 are the two equivalent ratios of 3: 5. 10. Short Answer: 1. ∴ They are equivalent ratios. 2. Sum = 2 + 3 = 5 ∴ First part = 2/5 × 60 =24 5 ∴ Second part =3/5 × 60 =36 5 Thus, the required two parts = 24 and 36. 3. 4. Total money deposited = ₹ 2050 Amount of money withdrawn = ₹ 410 Amount of money left in the bank = ₹ 2050 – ₹ 410 = ₹ 1640 (a) Ratio of money withdrawn to the total money deposited ∴ Required ratio = 1: 5 (b) Ratio of money withdrawn to the money left in the bank ∴ Required ratio = 1: 4 5. Total number of students = 180 Number of girls = 75 Number of boys = 180 – 75 = 105 ∴ Ratio of number of girls to the number of boys Required ratio = 5: 7 6. Here, sum of ratios = 2 + 7 + 1 = 10 ∴ Total quantity of green paint = 64 litres Quantity of blue paint =2/10× 64 = 12.8 litres Therefore, the required blue paint = 12.8 litres. 7. (a) Number of squares = 2 Number of triangles = 3 2 ∴ Ratio =2/3 or 2: 3 (b) Number of circles = 3 Number of rectangles = 3 ∴ Ratio =3/3 or 1: 1 Long Answer: 1. (a) Number of shaded parts = 4 Number of unshaded parts = 12 Required ratio = 1: 3 (b) Number of shaded parts = 2 Number of unshaded parts = 4 Required ratio = 1: 2 2. We have 20, 25, 12, 15 Product of extremes = 20 × 15 = 300 Product of middles = 25 × 12 = 300 Since both the products are same. ∴ The four numbers 20, 25, 12, 15 are in proportion. 3. Let the third term be x. ∴ 32, 112, x and 217 are in proportion. ∴ 32: 112:: x: 217 Thus, the third term = 62. 4. (a) Since 8, x, x, 50, are in proportion. ∴ x × x = 8 × 50 ⇒ x2 = 400 ∴ x = 20 (b) Since 36, 90, 90, x are in proportion. ∴ 36 × x = 90 × 90 ⇒x=(90×90)/36=225 ∴ x = 225 5. Number of tables purchased in ₹ 7500 = 10 Number of tables purchased in ₹ 1 =10/7500 ∴ Number of tables purchased in ₹ 9000 =(10×9000)/75000=12 6. Number of pens in 1 packet = 12 Number of pens in 39 packets = 12 × 39 = 468 Number of pens in 1 packet = 10 Number of pens in 52 packets = 10 × 52 = 520 Now cost of 468 pen = ₹ 374.40 Assertion and Reason Answers: (1) (a) A is false but R is true (2) (b) Both A and R are true and R is the correct explanation of A