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.