The salaries of P, Q, and R are in the ratio 5 : 8 : 6 and their expenses are in the ratio 4 : 7 : 5. If P saves 1/3rd of his salary then the savings of P, Q, and R are in the ratio of-

Question: The salaries of P, Q, and R are in the ratio 5 : 8 : 6 and their expenses are in the ratio 4 : 7 : 5. If P saves 1/3rd of his salary then the savings of P, Q, and R are in the ratio of-

Solution:
Let the salaries of P, Q and R are 5x, 8x, and 6x respectively
and expenses of P, Q and R are 4y, 7y and 5y respectively
ATQ,
5x - 4y = 5x × 1/3
⇒ 15x - 12y = 5x
⇒ 10x = 12y
⇒ x : y = 12 : 10

∴ The ratio of savings of P, Q, and R
= (5x - 4y) : (8x - 7y) : (6x - 5y)
= (5 × 12 - 4 × 10) : (8 × 12 - 7 × 10) : (6 × 12 - 5 × 10)
= (60 - 40) : (96 - 70) : (72 - 50)
= 20 : 26 : 22
= 10 : 13 : 11
Therefore, the savings of P, Q, and R are in the ratio 10 : 13 : 11