Question

The weight of 72 books is 9kg.1) find the weight of 80such books.2)how many books will weight 6kg.​

Answer 1

$\textbf{\large{\underline{Answer :-}}}$

1) ${\sf{The \:80\:books \: weight \: 10 \: kg}}$

2) ${\sf{48 \: books \: weight \: 6kg}}$

$\textbf{\large{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given : }}}$

Weight of the 72 books = 9kg

$\textsf{\underline{\underline{To find :}}}$

1) weight of 80 such books

2) number of books weight 6kg.

$\textsf{\underline{\underline{Solution :}}}$

By Proportion :-

Consider the weight of 80 books as x

↠ 72 : 9 : : 80 : x

★ As we know :

$\boxed{\sf{Mean \times Mean\:Terms = Extreme \times Extreme \:Terms}}$

$\textbf{Mean Terms}$ = 9 and 80

$\textbf{Extreme Terms}$ = 72 and x

$\sf{\implies}9 \times 80 = 72 \times x \\ \\ \sf{\implies}720 = 72x \\ \\ \sf{\implies}x =\frac{720}{72}\\ \sf{\implies}x = 10$

$\boxed{\sf{x = 10}}$

$\therefore{\sf{The \:80 \:books \: weight \: 10 \: kg}}$

2)

By Proportion :

Consider the books in 6 kg as x

↠ 72 : 9 : x : 6

$\boxed{\sf{Mean \times Mean\:Terms = Extreme \times Extreme \:Terms}}$

$\textbf{Mean Terms}$ = 9 and x

$\textbf{Extreme Terms}$ = 72 and 6

$\sf{\implies}9 \times x = 72 \times 6 \\ \\ \sf{\implies}9x = 432 \\ \\ \sf{\implies}x = \dfrac{432}{9}\\ \\ \sf{\implies}x = 48$

$\boxed{\sf{x = 48}}$

$\therefore{\sf{48\:books\:weight\:6kg}}$

Answer 2

72 Books=9 kg

Let Weight of 1 book=X kg

Then

72×weight of 1 book=9kg

72x=9

X=9/72

Means Weight of 1 Book=9/72 Kg

(a)If 1 book Weight=9/72 kg

9/72×80

=1/8×80

=10 kg

Weight of 80 books=10 kg.

(b) Let we can buy X books in 1 kg.

Then in 6kg=6x books

In 9kg We can Buy=9x books

Given we can buy in 9 kg 72

Means

9x=72

X=72/9

X=8

We get Value of X=8

Total Book in 6 kg=6x=6×8=48 books

$\boxed{\mathbf{\huge{(a).10\:kg}}}$

$\boxed{\mathbf{\huge{(b).48\:books}}}$