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Question 21 & 22

Question 21: Two Rawalpindi -Islamabad bus tickets and three Rawalpindi – Murree tickets cost Rs 770, but three Rawalpindi – Islamabad tickets and two Rawalpindi – Murree tickets cost Rs 730. What are tariffs from Rawalpindi to cities of Islamabad and Murree ?

FPSC AD IB 2017 (Calculate the total amount of money to be paid)

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Solution:

Let fare ticket Rawalpindi – Islamabad = x

ticket Rawalpindi – Murree = y

Now we are given ;

 Two bus tickets from Rawalpindi to Islamabad and three tickets from Rawalpindi to Murree cost Rs.770

\Rightarrow 2x+3y=770 ----(1)

and given that;

Three ticket from Rawalpindi to Islamabad and two tickets from Rawalpindi to Murree cost Rs. 730

\Rightarrow 3x+2y=730 ----(2)

Multiplying both sides of equations ‘1’ & ‘2’ with 2 and 3 respectively, then

we get ;

6x+9y=2310

6x+4y=1460

Subtracting these equations;

\Rightarrow 5y =850\Rightarrow y =170

\Rightarrow y =170

So fare from Rawalpindi to Murree is Rs 170

Now put this value of y in eq 1 or eq 2 (we put in eq 1);

2x + 3(170)=770

 \Rightarrow 2x + 510=770

 \Rightarrow 2x = 770-510 = 260

 \Rightarrow x = \frac{260}{2}=130

So , fare from Rawalpindi to Islamabad is Rs 130

Question 22 : Children’s tickets are sold at half price verusus adults. Five adult tickets and eight childrens’s tickets worth Rs 27 are sold. Find what adult’s ticket price is ?

FPSC AD IB 2017

Solution:

Here it is given that two children are equale to one adult . If we take ‘C’ for children and ‘A’ for adults then we can make an equation;

2 C = 1 A -------(1)

Further 5 adults and 8 children are buying tickets worth 27 Rs. So we can write an other equation;

5A+8C=27 ----- (2)

We can write it as under as well;

5A+4(2C)=27 ----- (3)

Now put value of 2C=A from eq (1) in eq (3);

\Rightarrow 5A+4(A)=27

\Rightarrow 5A+4A=27

\Rightarrow 9A=27

\Rightarrow A=3

 So, ticket for adult is worth Rs 3/-

 

 

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