# Comparing and Ordering Numbers

1) Daniel Is Managing a 1600-Unit Apartment Complex. Currently, 800 Units Are Rented at Rs 3000 per Month. A Market Survey Has Indicated That if He Decreases the Rent by Rs 50 per Month, He Can Give 100 More Units in Rent. If the Maintenance of the Apartment Is Rs 1000 per Month, Then Find a Profitable Deal.

Daniel gets Rs 3000 per month as rent for 800 units.
The maintenance of the apartment is Rs 1000.
So, the net income from the 800 units of the apartment is
Rs 3000 – Rs 1000 = Rs 2000

If he decreases the rent by Rs 50 per month, he can give 100 more units in rent.
Now, the rent is
Rs 3000 – Rs 50 = Rs 2950
He can give in rent
800 + 100 units = 900 units
So, now his net income from the 900 units of the apartment is
Rs 2950 – Rs 1000 = Rs 1950

Now, 2000 > 1950
So, the first deal was more profitable.

2) A City Transit System Carries 2000 Bus Riders per Day for a Fare of Rs 16. A Survey Indicates That the Number of Riders Will Increase by 400 People Every Day if the Fare Is Decreased by Rs 1 the Fare. Now, the Expenses for the Maintenance of the Bus per Day Are Rs 1500. Which Fare Is Less Profitable?

The daily net income of the bus when it carries 2000 bus riders each day with a fare of Rs 16 is
2000 × Rs 16 = Rs 32000
The daily profit of the bus, in this case, is
Rs 32000 – Rs 1500 = Rs 30500

If the fare is decreased by Rs 1, then the food is
Rs 16 – Rs 1 = Rs 15
If the number of riders increases by 400, then the number of riders now are
2000 + 400 = 2400

The daily net income of the bus, when it carries 2400 bus riders each day for a fare of Rs 16, is
2400 × Rs 15 = Rs 36000
The daily profit of the bus, in this case, is
Rs 36000 – Rs 1500 = Rs 31000
Rs 31000 > Rs 30500
So, the decreased fare is more profitable for the bus owners.