Q) A person on tour has Rs. 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by Rs.180. Find the original duration of the tour and daily expense.

(Q 34A – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let the original duration of the tour be x days and the original daily expenses are Rs. y / day

From the 1st condition, total expenses are Rs. 5,400

∴ x . y = 5,400

∴ y =

Step 2: From the 2nd condition, when the tour duration increased by 5 days, the daily expenses decreased by Rs. 180/day.

∴ ( x + 5).(y – 180) = 5,400

By substituting the value of y, we get:

∴ ( x + 5).( – 180) = 5,400

∴ ( x + 5). = 5,400

∴ ( x + 5).(5400 – 180 x) = 5,400 x

Dividing both sides by 30, we get:

∴ ( x + 5).(30 – x) = 30 x

∴ 30 x – x ² + 150 – 5 x = 30 x

∴ – x ² – 5 x + 150 = 0

∴ x ²+ 5 x – 150 = 0

Step 3: By mid-term splitting:

∴ x ² + 15 x – 10 x – 150 = 0

∴ x (x + 15) – 10 (x + 15) = 0

∴ (x + 15) (x – 10) = 0

∴ x = – 15 and x = 10.

Step 4: Here, since x is the duration in days, hence it can not be negative.

∴ we reject x = – 15 and accept x = 10

From equation (i), y = = 540

Therefore, the original duration of the tour is 10 days and the original daily expenses are Rs. 540 / day

Check: Let’s check validity of our solution at these values of x = 10 and y = 540
Here, x . y = 10 x 540 = 5400 ..1st condition is matched
Next, x + 5 = 10 + 5 = 15 and y – 180 = 540 – 180 = 360.
(x + 5). (y – 180) = 15 x 360 = 5400… 2nd condition is matched.
Since both conditions are matched, our solution is correct.

Please press the “Heart” button if you like the solution.