a person on a tour has Rs.9600 for his expenses.if his tour is extended by 16 days,he has to cut down his expenses by Rs.20 per day.what is his original duration of tour Related: Equations and Matrices (Part - 3)?

Question

a person on a tour has Rs.9600 for his expenses.if his tour is extended by 16 days,he has to cut down his expenses by Rs.20 per day.what is his original duration of tour Related:  Equations and Matrices (Part - 3)?

Answer

Solution:

Let the original duration of the tour be x days.

Then, he spent Rs. 9600 in x days.

If the tour is extended by 16 days, then the total duration of the tour becomes (x + 16) days.

In this case, he has to cut down his expenses by Rs. 20 per day. So, his new daily expenses become (old daily expenses - 20).

Therefore, the total expenses in (x + 16) days become:

9600 = x * old daily expenses + 16 * (old daily expenses - 20)

Simplifying the above equation, we get:

9600 = x * old daily expenses + 16 * old daily expenses - 320

9920 = x * old daily expenses + 16 * old daily expenses

9920 = (x + 16) * old daily expenses

old daily expenses = 9920 / (x + 16)

Now, we know that he spent Rs. 9600 in x days at the old daily expenses rate.

So, we can write:

9600 = x * old daily expenses

Substituting the value of old daily expenses, we get:

9600 = x * (9920 / (x + 16))

Multiplying both sides by (x + 16), we get:

9600 * (x + 16) = x * 9920

9600x + 153600 = 9920x

320x = 153600

x = 480

Therefore, the original duration of the tour is 480 days.

Answer

9600 ÷ 20 = 480
There are 16 days cancelled
so the tour is for 496(480 + 16) days.

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