generis wrote:

selim wrote:

The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4

B) 4 : 9

C) 2 :3

D) 3 : 2

E) 2 : 1

The purposely NOT fancy way.

Everything is defined in terms of pens and pencils. Take the ratio of pens and pencils and define one in terms of the other.

(1) 4 pens cost the same as 6 pencils

4 PN = 6 PC

6 PC = 4 PN

PC = \(\frac{4}{6}=\frac{2}{3}\)PN

(2) One CD costs the same as 4 pencils

1CD = 4PC

CD cost in

PNs?

From above, PC = \(\frac{2}{3}\) PN

So 1CD = (4 *\(\frac{2}{3}\)PN)

1 CD = \(\frac{8}{3}\) PN

(3) One book cost the same as 6 pens

1B = 6PN

(4) Book and CD cost in terms of PENS

1B = 6PN

1CD = \(\frac{8}{3}\)PN

(5) Ratio of book cost to CD cost?

\(\frac{B}{CD}=\frac{6}{(\frac{8}{3})}=(6*\frac{3}{8})=\frac{18}{8}=\frac{9}{4}\)

Answer A

Given,

4 Pen = 6 Pencil

=> 1 Pen = 6/4 Pencil

=> 1 Pen = 3/2 Pencil ..... Equation 1

Also given,

1 Book = 6 Pen ...... Equation 2

And

1 CD = 4 Pencil ....... Equation 3

We need to find out below ratio

Book : CD

Substitute the value of Book and CD in terms of Pen and Pencil from equation 2 and 3 respectively

=> 6 Pen : 4 Pencil

=> 1 Pen : 4/6 Pencil

=> 1 Pen : 2/3 Pencil

Substitute the value of 1 Pen in terms of Pencil from equation 1

=> 3/2 Pencil : 2/3 Pencil

=> 9 Pencil : 4 Pencil

Cancel the Pencil form both the sides

=> 9 : 4

Hence, the expected ratio is 9:4.

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