Salaries of Ram and Sam are in the ratio 7:8, and their savings are in the ratio 4:5. If Sam spends half of his income, then what is the ratio of their expenditures?
Answers
Given: Ratio of salaries of Ram and Sam= 7:8
Ratio of savings of Ram and Sam= 4:5
Expenditure of Sam is equal to half of his income
To Find: Ratio of their expenditures
Solution: Let the income of Ram and Sam be 7x and 8x respectively and the savings of Ram and Sam be 4y and 5y respectively.
Expenditure of Sam = 1/2 x Income of Sam (Given)
⇒ 8x - 5y = 1/2 x 8x
⇒ 4x = 5y ⇒ x:y = 5:4
Ratio of expenditure of Ram and Sam = (7x - 4y) : (8x - 5y)
⇒ (7x5 - 4x4) : (8x5 - 5x4)
⇒(35 - 16) : (40 - 20)
⇒ 19 : 20
Hence, the ratio of expenditure of Ram and Sam are in the ratio of 19:20
Given : Salaries of Ram and Sam are in the ratio 7:8, and their savings are in the ratio 4:5.
Sam spends half of his income
To Find : ratio of their expenditures
Solution:
Assume that :
Salary of Ram = 7S
=> Salary of Sam = 8S
Sam spends half of his income, = (1/2)8S = 4S
Sam Saving = 8S - 4S = 4S
Saving of Ram / Saving of Sam = 4/5
=> Saving of Ram /4S = 4/5
=> Saving of Ram = 16S/5
=> Saving of Ram = 3.2S/5
Ram Expenditure = 7S - 3.2S = 3.8S
ratio of their expenditures = 3.8S : 4S
=> 38 : 40
=> 19 : 20
ratio of their expenditures are 19 : 20
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