Question

The ratio of a's and b's income last year was 3:4. the ratio of their own incomes of last year and this year is 4:5 and 2:3 respectively. if the total sum of their present incomes is rs.4160, then find the present income of

a.

Answer 1

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Answer 2

Present income of a is Rs. 1600.

• Ratio of a's and b's income last year is 3:4.
• Let common multiple be x.
• a's last year income is 3x and b's last year income is 4x.
• Ratio of a's income last year and this year is 4:5.
• Let the common multiple be y.
• a's last year income is 4y and a's present income is 5y.

3x = 4y   (Equation 1)

• Ratio of b's income last year and this year is 2:3.
• Let the common multiple be z.
• b's last year income is 2z and b's present income is 3z.

4x = 2z   (Equation 2)

• Total sum of their present income = 4160

5y + 3z =  4160   (Equation 3)

• We have to find the present income of a. The present income of a is 5y, we have to find the value of y.

• Using the equation 3 we have to find the value of y, we write z in terms of y,

• Using equation 1 and equation 2, we get

x = 4y/3 = z/2

z = 8y/3     (Equation 4)

• Substituting the value of z in equation 3, we get

5y + 8y = 4160

13y = 4160

y = 320

• Now the present income of a is 5y.

• Therefore 5y = 1600 .
• Present income of a is Rs. 1600.