Which of the following statements are true?
(i) 51 : 68 = 85 : 102
(ii) 1.5 : 2.5 = 3.6 : 6
(iii) 30 bags : 18 bags = ₹ 450 : ₹ 270
(iv) 32 kg : ₹ 36 = 8 kg : ₹ 9

Question

Which of the following statements are true? (i) 51 : 68 = 85 : 102 (ii) 1.5 : 2.5 = 3.6 : 6 (iii) 30 bags : 18 bags = ₹ 450 : ₹ 270 (iv) 32 kg : ₹ 36 = 8 kg : ₹ 9

KnowledgeBoat · Accepted Answer

(i) False Reason — First Ratio (51 : 68): Let us find H.C.F. of 51 and 68: H.C.F. is 17. Simplest form: Second Ratio (85 : 102): Let us find H.C.F. of 85 and 102: H.C.F. is 17. Simplest form: Since 3:4 ≠ 5:6, the statement is False. (ii) True Reason — First Ratio = 1.5 : 2.5 Multiply by 10 to remove decimals = (1.5 x 10 : 2.5 x 10) = 15 : 25 Let us find H.C.F. of 15 and 25: H.C.F = 5 Simplest form: Second Ratio = 3.6 : 6 Multiply by 10 to remove decimals = (3.6 x 10 : 6 x 10) = 36 : 60 Let us find H.C.F. of 36 and 60: H.C.F. = 12. Simplest form: Since both simplify to 3:5, the statement is True. (iii) True Reason — First Ratio = 30 : 18 Let us find H.C.F. of 30 and 18: H.C.F. = 6. Simplest form: Second Ratio = 450 : 270 First, cancel the zeros: 45 : 27. Let us find H.C.F. of 45 and 27: H.C.F. = 9. Simplest form: Since both simplify to 5:3, the statement is True. (iv) False Reason — First Ratio = 32 : 36 Let us find H.C.F. of 32 and 36: H.C.F. = 4. Simplest form: Second Ratio = 8 : 9 This is already in its simplest form: So numerically both ratios are equal. But a ratio should exist only between quantities of the same kind. Here the quantities are kg and ₹, which are different kinds. Therefore the statement is false.

Mathematics

Which of the following statements are true?
(i) 51 : 68 = 85 : 102
(ii) 1.5 : 2.5 = 3.6 : 6
(iii) 30 bags : 18 bags = ₹ 450 : ₹ 270
(iv) 32 kg : ₹ 36 = 8 kg : ₹ 9

Ratio Proportion

Related Questions

Mathematics

Which of the following statements are true?(i) 51 : 68 = 85 : 102(ii) 1.5 : 2.5 = 3.6 : 6(iii) 30 bags : 18 bags = ₹ 450 : ₹ 270(iv) 32 kg : ₹ 36 = 8 kg : ₹ 9

Ratio Proportion

Related Questions

Which of the following statements are true?
(i) 51 : 68 = 85 : 102
(ii) 1.5 : 2.5 = 3.6 : 6
(iii) 30 bags : 18 bags = ₹ 450 : ₹ 270
(iv) 32 kg : ₹ 36 = 8 kg : ₹ 9