7 audio cassettes and 3 video cassettes cost Rs. 1110, while 5 audio cassettes and 4 video cassettes cost Rs.1350. Find the cost of an audio cassette and a video cassette respectively.

A
Rs. 30 and Rs. 300
B
Rs. 40 and Rs. 400
C
Rs. 20 and Rs. 300
D
Rs.30 and Rs. 500

Solution:

We have been given that 7 audio cassettes and 3 video cassettes cost Rs.1110, while 5 audio cassettes and 4 video cassettes cost Rs.1350.
We need to find the cost of an audio cassette and a video cassette.
Let x be the cost of an audio cassette and y be the cost of a video cassette.
Then, using the given conditions, the equations are,

7 x + 3 y = 1110

And,

5 x + 4 y = 1350

Find the value of x from the equation

7 x + 3 y = 1110

7 x + 3 y = 1110

\Rightarrow 7 x = 1110 - 3 y

\Rightarrow x = \frac{1110 - 3 y}{7}

Substitute

\frac{1110 - 3 y}{7}

for x in equation

5 x + 4 y = 1350

to find the value of y.

5 x + 4 y = 1350

\Rightarrow 5 (\frac{1110 - 3 y}{7}) + 4 y = 1350

\Rightarrow \frac{5550 - 15 y}{7} + 4 y = 1350

\Rightarrow 5550 - 15 y + 28 y = 9450

\Rightarrow 13 y = 9450 - 5550

\Rightarrow 13 y = 3900

\Rightarrow y = 300

Hence, the cost of a video cassette is Rs. 300.
Substitute 300 for y in equation

x = \frac{1110 - 3 y}{7}

to calculate the value of x.

\Rightarrow x = \frac{1110 - 3 y}{7}

\Rightarrow x = \frac{1110 - 3 (300)}{7}

\Rightarrow x = \frac{1110 - 900}{7}

\Rightarrow x = \frac{210}{7}

\Rightarrow x = 30

Hence, the cost of an audio cassette is Rs. 30.
Hence, the cost of an audio cassette is Rs. 30 and cost of a video cassette is Rs. 300.
Hence, option 1 is correct.