Question

In a month of twenty eight days, Rohan spends ₹x per day and saves ₹y per week for the first two weeks and he spends ₹2x per day and saves ₹0.5y per week in the last two weeks. What will be the algebraic expression that represents Rohan’s income this month?

• A. 42x + 3y
• B. 6x + 3y
• C. 42x + 21y
• D. 21x + 1.5y

Answer 1

The correct option is A 42x + 3y

Rohan spends ₹x per day and saves ₹y per week for the first two weeks.
So, as per the statement,
Total money that he spends in first two weeks
$=14\times Moneyspendperday=14x[\because 2weeks=14day]$

Total money he saves in first two weeks $=2\times Moneysaveperweek=2y$

$⟹$ The algebraic expression for Rohan’s income in first two weeks would be,
$14x+2y$

Now,
He spends ₹2x per day and saves ₹0.5y per week in the last two weeks,
So, as per the statement,

Total money that he spends in last two weeks
$=14\times Moneyspendperdayinlasttwoweeks=14\times 2x=28x[\because 2weeks=14day]$

Total money he saves in last two weeks $=2\times Moneysaveperweekinlasttwoweeks=2\times 0.5y=y$

$⟹$ The algebraic expression for Rohan’s income in last two weeks would be,
$28x+y$

So, the total income of Rohan would be,
Money that he earns in first two weeks + Money that he earns in last two weeks
$(14x+2y)+(28x+y)$
Step 1:
Open brackets and group the like terms,
$⟹(14x+2y)+(28x+y)⟹(14x+28x)+(2y+y)$
Step 2:
Solve the brackets,
$⟹42x+3y$

Hence, option (a) is correct.