# The total cost of six books, five pencils and seven sharpeners is Rs. 115 and that of eight books,

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The total cost of six books, five pencils and seven sharpeners is Rs. 115 and that of eight books, ten pencils and fourteen sharpeners is Rs. 190. Then which of the following article’s cost can be found uniquely

A) Pencil

B) Book

C) Sharpener

D) Cannot say

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Correct option is (B) Book

Let the cost of 1 book, 1 pencil and 1 sharpener is Rs. x, y & z respectively.

$\therefore$ According to given conditions

6x + 5y + 7z = 115              _________(1)

and 8x + 10y + 14z = 190   _________(2)

Multiply equation (1) by 2, we get

12x + 10y + 14z = 230       _________(3)

Subtract equation (2) from (3), we get

4x = 230 - 190 = 40

$\Rightarrow$ x = $\frac{40}4$ = 10 which is cost of 1 book.

From (2) given equations we can found only the value of x, because after substituting the value of x, we get two equations which are coincide. Therefore, we can not found the value of y & z.

Hence, only book's cost can be found uniquely.

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Correct option is B) Book