Below are three problems on linear equations. You have to form the equations by using the given information.

A railway half ticket( for kids below 5 years) costs Rs. 150 and full ticket(for above 5 years) costs Rs. 250. The daily report says that for a particular day, 5000 passengers have travelled and the total collection is Rs.10,50,000. How many kids(below 5 years) have travelled on that day?

a)1000 b)2000 c)2500 d)3500

Solution:

Let 's' be the number of kids travelled on that day and 'b' be the number of passengers(above 5 years) travelled on that day.

Therefore, s + b = 5000 ... eqn (1)

Each half ticket's cost is Rs.150 and

Each full ticket's cost is Rs.250.

Total collection of amount = 150s + 250b = 10,50,000

Or 150s + 250b = 10,50,000 ... eqn (2)

Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)

Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000

Or b = 3000

We know that s + b = 5000

So, s = 5000 - b = 5000 - 3000 = 2000.

Hence, 2000 kids travelled on that particular day.

Small sized pizza costs half the full sized and delivery charge is the same on small size as on the full size. One boy delivered a full size pizza which cost Rs.2160 for the consumer. Another boy delivered one full and small for 2 persons respectively where the bill amount was Rs.3270. What is the basic cost of full size pizza and what is the delivery charge?

a)RS.2100 & Rs.60 b)Rs.1050 & Rs.30 c)Rs.2500 & Rs.90 d)Rs.1500 & Rs.60

Solution:

Let the cost of the half of the full size pizza be Rs. X.

Therefore, the cost of full size pizza is Rs. 2X.

Let the delivery charge be Rs. Y per delivery.

Now, one full size reservation pizza would cost 2X (basic cost) + Y (delivery charge)

i.e., 2X + Y = 2160 --- (1)

The total basic cost for one small and one size full pizza = X + 2X = 3X and the total delivery charge is 2Y.

Hence, 3X + 2Y = 3270 --- (2)

Solving (1) and (2) we get,

X = 1050 and Y = 60

Hence, the basic cost of full size pizza is 2X = Rs. 2100 and the delivery charge is Y = Rs.60.

A boy ordered 1000 toys for 1000 rupees from a local shop. He knew he ordered some dolls, cars and cleversticks but he lost his receipt and forgot how many of each he ordered. Also he knew that the dolls were Rs.3 each, cars Rs.10 each and cleversticks Rs.5 each. The number of toy cars in the order was:

a)1 b)2 c)none of these d)cannot be determined

Solution:

Let d = number of dolls;

c = number of cars;

And s = number of cleversticks.

The total number of toys is 1000. Therefore we have the equation:

d + c + s = 1000

Given that the dolls cost Rs.3 each, cars cost Rs.10 each and cleversticks cost Rs.5.

Then we have the equation:

10c + 3d + 5s = 1000

Now, We have two equations but 3 unknowns. To solve 3 unknowns at least 3 equations are required.

The given data is not sufficient to derive the answer and some additional information are required.

Hence the answer is option d.

**Question 1**A railway half ticket( for kids below 5 years) costs Rs. 150 and full ticket(for above 5 years) costs Rs. 250. The daily report says that for a particular day, 5000 passengers have travelled and the total collection is Rs.10,50,000. How many kids(below 5 years) have travelled on that day?

a)1000 b)2000 c)2500 d)3500

**Answer :**b)2000Solution:

Let 's' be the number of kids travelled on that day and 'b' be the number of passengers(above 5 years) travelled on that day.

Therefore, s + b = 5000 ... eqn (1)

Each half ticket's cost is Rs.150 and

Each full ticket's cost is Rs.250.

Total collection of amount = 150s + 250b = 10,50,000

Or 150s + 250b = 10,50,000 ... eqn (2)

Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3)

Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000

Or b = 3000

We know that s + b = 5000

So, s = 5000 - b = 5000 - 3000 = 2000.

Hence, 2000 kids travelled on that particular day.

**Question 2**Small sized pizza costs half the full sized and delivery charge is the same on small size as on the full size. One boy delivered a full size pizza which cost Rs.2160 for the consumer. Another boy delivered one full and small for 2 persons respectively where the bill amount was Rs.3270. What is the basic cost of full size pizza and what is the delivery charge?

a)RS.2100 & Rs.60 b)Rs.1050 & Rs.30 c)Rs.2500 & Rs.90 d)Rs.1500 & Rs.60

**Answer :**a)Rs.2100 & Rs.60Solution:

Let the cost of the half of the full size pizza be Rs. X.

Therefore, the cost of full size pizza is Rs. 2X.

Let the delivery charge be Rs. Y per delivery.

Now, one full size reservation pizza would cost 2X (basic cost) + Y (delivery charge)

i.e., 2X + Y = 2160 --- (1)

The total basic cost for one small and one size full pizza = X + 2X = 3X and the total delivery charge is 2Y.

Hence, 3X + 2Y = 3270 --- (2)

Solving (1) and (2) we get,

X = 1050 and Y = 60

Hence, the basic cost of full size pizza is 2X = Rs. 2100 and the delivery charge is Y = Rs.60.

**Question 3**A boy ordered 1000 toys for 1000 rupees from a local shop. He knew he ordered some dolls, cars and cleversticks but he lost his receipt and forgot how many of each he ordered. Also he knew that the dolls were Rs.3 each, cars Rs.10 each and cleversticks Rs.5 each. The number of toy cars in the order was:

a)1 b)2 c)none of these d)cannot be determined

**Answer :**d)cannot be determinedSolution:

Let d = number of dolls;

c = number of cars;

And s = number of cleversticks.

The total number of toys is 1000. Therefore we have the equation:

d + c + s = 1000

Given that the dolls cost Rs.3 each, cars cost Rs.10 each and cleversticks cost Rs.5.

Then we have the equation:

10c + 3d + 5s = 1000

Now, We have two equations but 3 unknowns. To solve 3 unknowns at least 3 equations are required.

The given data is not sufficient to derive the answer and some additional information are required.

Hence the answer is option d.

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