Question

Drawing pencils cost 80 paise each and coloured pencils cost Rs 1.10 each. If altogether two dozen pencils cost Rs 21.60, how many coloured pencils are there?​

Answer 1

Answer:

Let the number of drawing pencils be x

And let the number of colored pencils be y

Then, according to the given conditions, we have

x + y = 2 x 12 [1 dozen = 12]

x + y = 24 … (i)

And,

x × 80/100 + y x 1.10 = 21.60 [As 80 paise = Rs 80/100]

80x/100 + 1.10y = 21.60

(80x + 110y)/100 = 21.60

80x + 110y = 2160

8x + 11y = 216 … (ii)

Performing 8 x (i) – (ii), we have

8x + 8y = 192

8x + 11y = 216

(-)--(-)----(-)-----

-3y = -24

y = -24/-3

y = 8

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

x + 8 = 24

x = 24 – 8

x = 16

Therefore, the number of colored pencils is y = 8

Answer 2

Step-by-step explanation:

Let the number of drawing pencils be x

Let the number of colour pencils be y

Altogether there are 2 dozens i.e, 2(12) = 24 number of pencils.

Total number of pencils = 24

x + y = 24

x = 24 - y -----eq(l)

Cost of each drawing pencil = 80Paise = 80/100 = Rs. 0.8 (Since Rs. 1 = 100 Paise)

Cost of drawing pencils = 0.8x = 0.8(24- y) = 19.2 - 0.8y(From (1))

Let the number of colour pencils be y

Cost of colour pencils = 1.1 x y = Rs. 1.1y

Total cost of colour pencils and drawing pencils = Rs. 21.6

19.2 - 0.8y + 1.1y = 21.6

0.3y + 19.2 = 21.6

0.3y = 21.6 - 19.2

0.3y = 2.4

y = 2.4/0.3

y = 24/3

y = 8