Question no.2 From ML aggarwal book, class10, chapter 7, ratio and proportion
We have been given two ratios in forms of a:b and c:d, and we have to find the compound ratio of them.
ML Aggarwal book
Avichal publication
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Find the compounded ratio of: (i) 2: 3 and 4: 9 (ii) 4: 5, 5: 7 and 9: 11 (iii) (a – b): (a + b), (a + b)2: (a2 + b2) and (a4 – b4): (a2 – b2)2
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Solution:
(i) 2: 3 and 4: 9
We know that
Compound ratio = 2/3 × 4/9
= 8/27
= 8: 27
(ii) 4: 5, 5: 7 and 9: 11
We know that
Compound ratio = 4/5 × 5/7 × 9/11
= 36/77
= 36: 77
(iii) (a – b): (a + b), (a + b)2: (a2 + b2) and (a4 – b4): (a2 – b2)2
We know that
Compound ratio = (a – b)/ (a + b) × (a + b)2/ (a2 + b2) × (a4 – b4)/ (a2 – b2)2
By further calculation
= (a – b)/ (a + b) × [(a + b) (a + b)]/ (a2 + b2) × [(a2 + b2) (a + b) (a – b)]/ [(a + b)2 (a – b)2]
So we get
= 1/1