Question

26. * (4x + 3y) : (3x + 5y) = 6: 7, find :
(1) Xy
(ii) x, if y = 10
(iii) y, if x = 27​

Answer 1

Solution:

(i) 7x (4x + 3y) = 6x (3x + 5y)

28x + 21y = 18x + 30y

28x – 18x = 30y – 21y

10x = 9y

x/y = 9/10

∴ x : y = 9 : 10

(ii) (4x + 3y) : (3x + 5y) = 6 : 7

Given, y = 10

∴ (4x + 3 × 10) : (3x + 5 × 10) = 6 : 7

(4x + 30) : (3x + 50) = 6 : 7

(4x + 30) : (3x + 50) = 6 : 7

7 × (4x + 30) = 6 × (3x + 50)

28x + 210 = 18x + 300

28x – 18x = 300 – 210

10x = 90

⇒ x = 90/10 = 9

(iii) (4x + 3y) : (3x + 5y) = 6 : 7

Given, x = 27

∴ (4 × 27 + 3y) : (3 × 27 + 5y) = 6 : 7

(108 + 3y) : (81 + 5y) = 6 : 7

7 × (108 + 3y) = 6 × (81 + 5y)

756 + 21y = 486 + 30y

9y = 270

⇒ y = 270/9 = 30

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