Question

3 chocolate bars and 4 ice cream cones cost Rs. 135. If the price of a chocolate bar increases by
5% and that of an ice cream cone increases by 10%, the total cost goes up by Rs. 9.75, find the
increased price of each chocolate bar and an ice cream cone.​

Answer 1

Given:

3 chocolate bars and 4 ice cream cones cost Rs. 135. If the price of a chocolate bar increases by 5% and that of an ice cream cone increases by 10%, the total cost goes up by Rs. 9.75,

To find:

The increased price of each chocolate bar and an ice cream cone.​

Solution:

Let,

"c" → represents the price of one chocolate bar

"i" → represents the price of ice-cream cones

So, the first equation will be as follows:

3c + 4i = 135 . . .  (1)

After the increase in prices:

The increased price of 1 chocolate bar = $c + \frac{5}{100} c = c + 0.05c = 1.05c$

∴ The increased price of 3 chocolate bars = $3 \times 1.05c = 3.15c$

and

The increased price of 1 ice-cream cone = $i + \frac{10}{100} i = i + 0.1i = 1.1i$

∴ The increased price of 4 ice-cream cones = $4 \times 1.1i = 4.4i$

The total cost becomes = Rs. 135 + Rs. 9.75 = Rs. 144.75

So, the second equation will be as follows:

3.15c + 4.4i = 144.75 . . .  (2)

On multiplying the equation (1) by 3.15 and equation (2) by 3, we get

9.45c + 12.6i = 425.25 . . .  (3)

and

9.45c + 13.2i = 434.25 . . . (4)

On subtracting equation (3) from (4), we get

9.45c + 13.2i = 434.25

9.45c + 12.6i = 425.25

-          -             -

--------------------------------------

         0.6i = 9

--------------------------------------

∴ i = 15

On substituting the value of i in equation (1), we get

3c + (4 × 15) = 135

⇒ 3c + 60 = 135

⇒ 3c = 75

⇒ c = 25

Thus,

The increased price of 1 chocolate bar is,

= 1.05c

= 1.05 × 25

= Rs. 26.25

and

The increased price of 1 ice-cream cone is,

= 1.1i

= 1.1 × 15

= Rs. 16.50

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