A basic and basic important ques from chapter 7 of ML aggarwal, ratio and proportion
We have given 3x + 5y/ 3x – 5y = 7/3, and we have to. find x: y.
(ii) If a: b = 3: 11, and we have to find (15a – 3b): (9a + 5b).
Question no. 11, ratio and proportion
Solution:
(i) 3x + 5y/ 3x – 5y = 7/3
By cross multiplication
9x + 15y = 21x – 35y
By further simplification
21x – 9x = 15y + 35y
12x = 50y
So we get
x/y = 50/12 = 25/6
Therefore, x: y = 25: 6
(ii) It is given that
a: b = 3: 11
a/b = 3/11
It is given that
(15a – 3b)/ (9a + 5b)
Now dividing both numerator and denominator by b
= [15a/b – 3b/b]/ [9a/b + 5b/b]
By further calculation
= [15a/b – 3]/ [9a/b + 5]
Substituting the value of a/ b
= [15 × 3/11 – 3]/ [9 × 3/11 + 5]
So we get
= [45/11 – 3]/ [27/11 + 5]
Taking LCM
= [(45 – 33)/ 11]/ [(27 + 55)/ 11]
= 12/11/ 82/11
We can write it as
= 12/11 × 11/82
= 12/82
= 6/41
Hence, (15a – 3b): (9a + 5b) = 6: 41.