Question

Need solution of both questions (3 and 4) !

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Answer 1

$\sf{\underline{\underline{ \purple{ \huge{Question:}}}}}$

From a $\sf{ 62 \dfrac{1}{2}}$ m long rope, a piece of length $\sf{ 15 \dfrac{1}{5}}$ m is cut off. The rest of the rope is divided into 11 equal pieces. Find the length of each equal piece.

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Given:}}}}}$

✰ Length of rope = $\sf{ 62 \dfrac{1}{2}}$ m

✰ Length of cutted piece = $\sf{ 15 \dfrac{1}{5}}$

✰ The rest of the rope is divided into 11 equal pieces.

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{To \: Find:}}}}}$

✠ The length of each equal piece.

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Solution:}}}}}$

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To find the length of each equal pieces we will subtract the length of the cutted piece from the total length of the rope. Then we will divided by 11, as the rest of the rope is divided into 11 equal parts to get the length of each equal part.

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The piece left when a piece of length $\sf{ 15 \dfrac{1}{5}}$ m is cut off from the rope

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$\\ \sf= 62 \dfrac{1}{2} - 15 \dfrac{1}{5}$

$\\ \sf= \dfrac{125}{2} - \dfrac{76}{5}$

$\\ \sf= \dfrac{625 - 152}{10}$

$\\ \sf= \dfrac{473}{10}$

$\\ \bf=47. 3 \: m$

Now, the length of of each equal piece when the rest of the rope is divided into 11 equal pieces.

$\\ \\ \sf = 47.3 \div 11$

$\\ \sf = \dfrac{47.3 }{11}$

$\\ \sf = \dfrac{ \cancel{{473}}^{43} }{ \cancel{11} \times 10}$

$\\ \sf = \dfrac{ 43 }{ 10}$

$\\ \bf =4.3 \: m$

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$\therefore{ \sf{The \: length \: of \: each \: equal \: piece = {\green{ \underline{ \boxed{ \sf{4.3 \: m}}}}}}}$

$\\ \\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Question:}}}}}$

Evaluate:

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$\blue{\bf i.)} \: \sf {{\bigg \{}{ \bigg(} {\dfrac{1}{2} { \bigg)} }^{ - 3} + { \bigg(} {\dfrac{1}{3} { \bigg)} }^{ - 2} { \bigg \}}}^{ - 1} \div { \bigg(} {\dfrac{1}{4} { \bigg)} }^{ - 1}</p><p></p><p>$

$\blue{ \bf{ii.)}} \sf By \: what \: number \: should \: {\bigg (}{ \dfrac{ - 6}{5} {\bigg )}}^{2} \: be \: divided \: so \: that \: the \: quotient \: is \: { \bigg(} { \dfrac{3}{5}{ \bigg)} }^{ - 1}$

$\\ \\ \\ \sf{\underline{\underline{ \purple{ \huge{Answer:}}}}}$

$\blue{\bf i.)} \: \sf {{\bigg \{}{ \bigg(} {\dfrac{1}{2} { \bigg)} }^{ - 3} + { \bigg(} {\dfrac{1}{3} { \bigg)} }^{ - 2} { \bigg \}}}^{ - 1} \div { \bigg(} {\dfrac{1}{4} { \bigg)} }^{ - 1}$

$\\ \\ \implies\sf {\{ {2}^{3} + {3}^{2} \}}^{ - 1} \div 4$

$\\ \\ \implies\sf {\{ 8+ 9 \}}^{ - 1} \div 4$

$\\ \\ \implies\sf {\{ 17 \}}^{ - 1} \div 4$

$\\ \\ \implies\sf \dfrac{1}{17} \div 4$

$\\ \\ \implies\sf \dfrac{1}{17} \times \dfrac{1}{4}$

$\\ \\ { \blue \implies\bf \dfrac{1}{68} }$

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$\therefore{ \sf{After \: evaluating \: we \: get \: = {\green{ \underline{ \boxed{ \bf{ \frac{1}{68} }}}}}}}$

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For answer of second part $\blue{\bf ii.)}$ refer the attachment ✓

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