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The pair of $3$ full tickets and two half tickets is $Rs . 204$ and the pair of two full tickets and $3$ half tickets are $Rs . 186$ . Find the cost of a pair of a full ticket and a half ticket.

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78 Rs

80 Rs

75 Rs

70 Rs

answer is A.

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Detailed Solution

Given,
Price of 3 full and two half tickets= Rs. 204
Suppose
Price of the full ticket

= Rs . x

Price of the half ticket

= Rs . y

Thus,

3 x + 2 y = 204

2 (3 x + 2 y) = 2 \times 204

6 x + 4 y = 408 . . . . . . . . . . . . . (1)

Now, price of two full tickets and

3

half tickets are

Rs . 186

. Thus,

2 x + 3 y = 186

3 (2 x + 3 y) = 3 \times 186

6 x + 9 y = 558 . . . . . . . . . . . (2)

Now, subtract equation

(1) from (2),

(6 x + 9 y) - (6 x + 4 y) = 558 - 408 \Rightarrow 5 y = 150 \Rightarrow y = \frac{150}{5} = 30 . . . . . . . . . . . . . (3)

Put the value of

y

in equation

(1)

, we get

6 x + 4 y = 408 \Rightarrow 6 x + 4 \times 30 = 408 \Rightarrow 6 x = 408 - 120 = 288 \Rightarrow x = \frac{288}{6} = 48 . . . . . . . . . . . . . . (4)

Price of a pair of full and half ticket

= 48 + 30

= Rs . 78

Hence, option 1 is correct.

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