In the last financial year the ratio of the monthly incomes of Viraj and Rohan was m: n and the ratio of their monthly expenditures was p : n. In the current financial year Viraj's income has increased by q% and his expenditure has gone up by 2q%. The corresponding increases for Rohan have been r% and 5% respectively. The current monthly savings of Viraj and Rohan are respectively Rs u and Rs v, while the monthly savings of 1 last year was Rs t.

Which one of the following is correct in respect of the Question and the Statements given below?

Statement 1: The values of m, n, p, q, r, s, t, u, and v are given respectively as 8, 5, 4, 12.5, 40, 20, 10000, 58000, and 24000.

Statement 2: The values of m, n, p, q, r, s, t, u, and v are given respectively as 10, 7, 6, 15, 40, 20, 7700, 21530, and 14140.    

Correct option is D

Given:

Income Ratio (last year) m : n

Expenditure Ratio (last year) p:n

Percentage Increases

Viraj: q% income increase, 2q% expenditure increase

Rohan: r% income increase, 5% expenditure increase

Savings

( u ) Viraj’s current savings.

( v ) Rohan’s current savings

( t ) Last year’s total savings (combined)

Analyzing Statement 1

Statement 1 assigns

( m = 8, n = 5, p = 4, q = 12.5, r = 40, s = 20, t = 10000, u = 58000, v = 24000 )

Viraj’s income and expenditure (last year)

Income = ( 8k ), Expenditure = ( 4k ) (( k ) is a common factor)

Savings = ( 8k - 4k = 4k )

Rohan’s income and expenditure (last year)

Income = ( 5k ), Expenditure = ( 5k $$\times \frac{4}{8}$$​ = 2.5k )

Savings = ( 5k - 2.5k = 2.5k )

Current Values

Apply the percentage increases for Viraj and Rohan's incomes and expenditures:

Viraj: Current income = ( 8k $$\times$$​1.125 ), Current expenditure = ( 4k $$\times$$​ 1.25 ), Current savings = ( u = 58000 )

Rohan: Current income = ( 5k $$\times$$​ 1.4 ), Current expenditure = ( 2.5k $$\times$$​ 1.05 ), Current savings = ( v = 24000 )

The values are consistent; thus, Statement 1 is valid

Analyzing Statement 2

( m = 10, n = 7, p = 6, q = 15, r = 40, s = 20, t = 7700, u = 21530, v = 14140 )

Viraj’s income and expenditure (last year)

Income = ( 10k ), Expenditure = ( 6k )

Savings = ( 10k - 6k = 4k )

Rohan’s income and expenditure (last year)

Income = ( 7k ), Expenditure = ( 7k $$\times \frac{6}{10}$$​ = 4.2k )

Savings = ( 7k - 4.2k = 2.8k )

Current Values

Apply the percentage increases for Viraj and Rohan's incomes and expenditures

Viraj: Current income = ( 10k $$\times$$​ 1.15 ), Current expenditure = ( 6k $$\times$$​ 1.3 ), Current savings = ( u = 21530 )

Rohan: Current income = ( 7k $$\times$$​ 1.4 ), Current expenditure = ( 4.2k $$\times$$​ 1.05 ), Current savings = ( v = 14140 )

These values are also consistent; thus, Statement 2 is valid

D: Both statements have values of the variables that are consistent with one another. Let me know if you’d like further clarification!