Question

in a library 136 copies of certain book require a shelf - length of 3.4 m.how many copies of the same book would occupy a shelf - length of 5.1m?​

Answer 1

Required Solution:

Here, in the question, the concept of direct proportion has been applied. In the question we are given that y 136 copies of certain book require a shelf - length of 3.4 m and we have to find out how many copies of the same book would occupy a shelf - length of 5.1 m.

Let us assume the number of required copies be x.

Table :

$\small\boxed {\begin{array}{c|c|c} \underline{\sf{Number \: of \: copies}} & \underline{\sf{ \: \: 136 \: \: }} & \underline{\sf{ \: x \: }} \\ \\ \underline{\sf{ \: \: \: Length \: (in\: m) \: \: }} & \underline{\sf{ \: \: 3.4 \: \: }} & \underline{\sf{5.1}}\end{array} }$

Here,

• More copies → More shelf length.
• So, here is direct proportion.

As the numbers of copies and length of the shelf are in direct proportion. So,

$\sf{ \longrightarrow \: \dfrac{136}{3.4} = \dfrac{x}{5.1} } \\ \\ \bigstar \: \underline { \boldsymbol{By \: cross \: multiplication - }} \\ \\ \sf{ \longrightarrow \:3.4x = 136 \times 5.1 } \\ \\ \\ \sf{ \longrightarrow \:x = \dfrac{ 136 \times 5.1}{3.4} } \\ \\ \\ \sf{ \longrightarrow \:x = \dfrac{ 136 \times 510}{340} } \\ \\ \\ \sf{ \longrightarrow \:x = \dfrac{ 136 \times 51}{34} } \\ \\ \\ \sf{ \longrightarrow \:x = \dfrac{ \cancel{136 }\times 510}{ \cancel{34}} } \\ \\ \\ \sf{ \longrightarrow \:x = \dfrac{ 8 \times 51}{2} } \\ \\ \\ \sf{ \longrightarrow \:x = 4 \times 51 } \\ \\ \\ \longrightarrow \underline{ \boxed{ \sf{x =204 }}} \: \: \red{ \bigstar}$

Henceforth, 204 copies of the same book would occupy a shelf - length of 5.1 m.

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⠀⠀⠀⠀⠀⠀⠀★ Note

$\sf{If \: x \: and \: y \: are \: in \: variation,then} \\ \\ \bull \: \: \: \sf{ \dfrac{x_1}{y_1} = \dfrac{x_2}{y_2} = \dfrac{x_3}{y_3} = \dfrac{x_n}{y_n} }$

Answer 2

Answer:

in a library 136 copies of certain book require a shelf - length of 3.4 m.how many copies of the same book would occupy a shelf - length of 5.1m?