Formulate the following problems as a pair of equations, and hence find their solutions:
Three chairs and two tables cost ₹ 700 and five chairs and three tables cost ₹1100. What is the total cost of 2 chairs and 3 tables?

Question

Formulate the following problems as a pair of equations, and hence find their solutions:
A train travelled a certain distance at a uniform speed. If the train had been 6 km/hr faster, it would have taken 4 hours less than the scheduled time. If the train were slower by 6 km/hr, then it would have taken 6 hours more than the scheduled time. Find the distance covered by the train.

Philoid · Accepted Answer

Let the speed be x km/hr and distance travelled be y km.

We know that distance = speed × time

Scheduled time to cover distance = y/x hr

Then the first condition is

⇒ = – 4

⇒ =

⇒ xy = (x + 6) (y – 4x)

⇒ xy = xy – 4x² + 6y – 24x

⇒ 4x² – 6y + 24x = 0

⇒ 2x² – 3y + 12x = 0 i.e. 12x – 3y + 2x² = 0

Second condition is

⇒ = + 6

⇒ =

⇒ xy = (x – 6) (y + 6x)

⇒ xy = xy + 6x² – 6y – 36x

⇒ 6x² – 6y – 36x = 0

⇒ x² – y – 6x = 0 i.e. – 6x – y + x² = 0

For cross multiplication method, we write the coefficients as

Hence, we get = =

⇒ = =

⇒ =

⇒ – 30x = – x²

⇒ 30km/hr = x

Now, =

⇒ =

⇒ y = 24 × 30 = 720 km

∴ The distance covered by train = 720 km