Question

The ratio of monthly income of A and B in the ratio is 6:5 and the ratio of their expenditure is 9:7.If each saves Rs.1500.Then the sum of their salary is​

Answer 1

GIVEn

The ratio of monthly income of A and B in the ratio is 6:5 and the ratio of their expenditure is 9:7.If each saves Rs.1500.

TO FINd

Find the salary of A and B

SOLUTIOn

✞ Let the income of A be 6x and B be 5x Now, let their expenditure be 9y and 7y

✑ According to the given condition

• Income = Expenditure + Saving
• 6x = 9y + 1500 { For A }
• 5x = 7y + 1500 { For B }

→ 6x - 9y = 1500 ---(i)

→ 5x - 7y = 1500 -----(ii)

✑ Multiply (i) by 5 and (ii) by 6

• 30x - 45y = 7500
• 30x - 42y = 9000

✑ Subtract both the equations

→ (30x - 45y) - (30x - 42y) = 7500 - 9000

→ 30x - 45y - 30x + 42y = -1500

→ - 3y = -1500

→ y = 1500/3 = 500

✑ Put the value of y in eqⁿ (ii)

→ 5x - 7y = 1500

→ 5x - 7×500 = 1500

→ 5x - 3500 = 1500

→ 5x = 3500 + 1500

→ 5x = 5000

→ x = 5000/5 = 1000

Hence,

Salary of A = 6x = 6 × 1000 = Rs.6000

Or

Salary of B = 5x = 5×1000 = Rs.5000

Answer 2

$\blue{\bold{\underline{\underline{Given}}}}$

• Ratio of income of A and B = 6:5

• Ratio of expenditure of A and B = 9:7

$\blue{\bold{\underline{\underline{ToFind}}}}$

• Sum of their salary

$\blue{\bold{\underline{\underline{Solution}}}}$

Let the ratio of their :-

• Income = 6x : 5x

• Expenditure = 9y : 7y

Now,

➠ 6x - 9y = 1500 ------➀

➠ 5x - 7y = 1500. -------➁

On multiplying Eq. (i) by 5 and Eq. (ii) by 6 to make the coefficients of x equal, we get

➠ 30x – 45y = 7500 …(3)

➠ 30x – 42y = 9000 …(4)

On subtracting Eq. (3) from (4), we get

↣ (30x - 42y) - (30x - 45y) = 9000 - 7500

↣ 10x - 10x - 42y + 45y = 1500

↣ 3y = 1500

↣ y = 500

On putting y = 500 in Eq. (1) , we get

↣ 6x – 9y = 1500

↣ 6x - 9×500 = 1500

↣ 6x - 4500 = 1500

↣ 6x = 1500 + 4500

↣ 6x = 6000

↣ x = 6000/6

↣ x = 1000

Thus,

Monthly income of both the persons are 6(1000) and 5(1000), i.e. Rs. 6000 and Rs. 5000

• Sum of their salary = 6000 + 5000 = 11000