The ratio of incomes of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs. 2600 and Rs.1800 respectively, their incomes are.
Correct Answer: Rs. 8000, Rs. 4800
Let the incomes of the two persons be 5x and 3x
and
their expenditures be 9y and 5y respectively.
Then,
= 5x - 9y = 2600.....(i)
= 3x - 5y = 1800.....(ii)
Multiplying (i) by 3 and (ii) by 5, we get:
= 15x - 27y = 7800.....(iii)
= 15x - 25y = 9000.....(iv)
Subtracting (iii) from (iv), we get : 2y = 1200 or y = 600
Putting y = 600 in (i), we get : 5x = 8000 or x = 1600.
∴ Their incomes are Rs. (5 × 1600) and Rs. (3 × 1600)i.e.
Rs. 8000 and Rs. 4800 respectively
and
their expenditures be 9y and 5y respectively.
Then,
= 5x - 9y = 2600.....(i)
= 3x - 5y = 1800.....(ii)
Multiplying (i) by 3 and (ii) by 5, we get:
= 15x - 27y = 7800.....(iii)
= 15x - 25y = 9000.....(iv)
Subtracting (iii) from (iv), we get : 2y = 1200 or y = 600
Putting y = 600 in (i), we get : 5x = 8000 or x = 1600.
∴ Their incomes are Rs. (5 × 1600) and Rs. (3 × 1600)i.e.
Rs. 8000 and Rs. 4800 respectively
