Question

Last year, the incomes of a, b and c were in the ratio of 4 : 3 : 5. The ratio of as income of last year to that of this year is 2 : 3. The corresponding ratio for b and c are 3 : 4 and 4 : 5 respectively. If the sum of their incomes this year is rs.819000, then the income, in rupees, of c this year exceeds that of a by

Answer 1

Answer

In rupees, of c this year exceeds that of a by Rs 12600                                                                                                          

Explanation

It is given that incomes of a, b and c were in the ratio of 4 : 3 : 5.

Let their income be 4x,3x,and 5x

Step 1: Find the raio of this year income

The ratio of as income of  in last year to that of this year is 2 : 3.

From this we get

4x/ this year income =2/3

Therefore a's this year income = 6x

The ratio of as income of b in last year to that of this year is3 : 4

3x/ this year income =3/4

Therefore a's this year income = 4x

The ratio of as income of c in last year to that of this year is 4 : 5

5x/ this year income =4/5

Therefore a's this year income = 25x/4

In this year ratio of income of a,b, and c is given by

a:b:c: = 6x : 4x : 25x/4 = 24 : 16 : 25

Step 2 : Calculate a's and c's this year income

If the sum of their incomes this year is rs.819000

a's income = (24/65 ) x 819000

c's income = (25/65 ) x 819000

Step 3: Find the difference in a's and c's this year income

In rupees, of c this year exceeds that of a by  (25/65 ) x 819000 - (24/65 ) x 819000 =819000/65 =Rs 12600

Answer 2

Last year: A : B : C = 4 : 3 : 2

Find the Ratio of A:

Ratio of last year income to this year income, A = 2 : 3

(Multiply by 2)

⇒ A = 4 : 6

Find the Ratio of B:

Ratio of last year income to this year income, B = 3 : 4

⇒ B = 3 : 4

Find the Ratio of C:

Ratio of last year income to this year income, C = 4 : 5

(Multiply by 5.4)

⇒ C = 5 : 25/4

Find the ratio this year:

This year = A : B : C = 6 : 4 : 25/4

(Multiply by 4)

⇒ A : B : C = 24 : 16 : 25

Solve x:

24x + 16x + 25x = Rsa 819000

65x = 819000

x = Rs 12600

Define y:

Let y be the constant ratio

Ratio of C = 4x : 5y

Difference in the income = 5y - 4y = y

Solve x:

4y = Rs 315000

y = 315000 ÷ 4 = Rs 78750

Answer: C exceeds last year by Rs 78750