type 4 income & expenditure based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Let incomes of A and B be Rs.3x and Rs.2x respectively.

Let the expenditures of A and B be Rs.5y and Rs.3y respectively.

According to the question,

3x - 5y = Rs. 1000 ... (i)

2x - 3y = Rs. 1000 ... (ii)

By equation (i) × 2 - (ii) × 3,

y = 1000

From equation (i),

3x - 5 × 1000 = 1000

3x = 1000 + 5000

= Rs.6000 = A’s income

Answer: (b)

Expenditure : Savings

= 61 : 6

Sum of the terms of ratio

= 61 + 6 = 67

Total monthly salary

= Rs.8710

Monthly savings

= Rs.$(6/67 × 8710)$ = Rs.780

Answer: (a)

If the ratio of the income of A and B be a : b

and that of their expenses be c : d and each saves x, then,

A’s income = ${ax(d - c)}/{ad - bc}$

= ${9 × 500(7 - 8)}/{9 × 7 - 8 × 8}$

= 9 × 500 = 4500

Answer: (d)

Income of the family

= $10/7 × 10500$ = Rs.15000

Savings = 15000 - 10500

= Rs.4500

Answer: (d)

Income of A = Rs.7x ;

B = Rs.9x and C = Rs.12x

Expenses of A = Rs.8y ;

B = Rs.9y and C = Rs.15y

7x - 8y = $1/4$ × 7x

7x - ${7x}/4$ = 8y

${21x}/4 = 8y$

21x = 32y.

A’s saving = $1/4 × 7x$

= $1/4 × 32/3 y = 8/3 y$

B’s saving = 9x - 9y

= $9 × 32/21 y - 9y$

= ${96y - 63y}/7 = {33y}/7$

C’s saving = 12 x - 15 y

= 12 × $32/21$ y - 15y

= ${128y - 105y}/7 = {23y}/7$

Required ratio

= $8/3y : 33/7y : 23/7y$

= 56 : 99 : 69