Question

Divide Rs,1380 among Ahmed, John, Babita so that amount Ahmed receives is 5 times as much as Babita's share and is 3 times as much as John's share.​

Answer 1

Question :-

• Divide Rs,1380 among Ahmed, John, Babita so that amount Ahmed receives is 5 times as much as Babita's share and is 3 times as much as John's share.

Solution :-

• Let Babita's share be Rs, x
• Then, Ahmed's share = Rs, 5x
• Jhon's share = Total Amount - (Babita's share + Ahmed's share )
• Jhon's Share = 1380 - (x + 5x ) = Rs, 1380 - 6x

It is given that Ahmed's share is 3 times Jhon's share

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Question :}} \\\end{gathered}\end{gathered}$

$\quad {:} \longrightarrow \sf \boxed{\bf{ 5x \: = \: 3 \: (1380 - 6x) }}$

$\quad {:} \longrightarrow \sf {\sf{ 5x \: = \: 4140 - 18x }}$

$\quad {:} \longrightarrow \sf {\sf{ 5x \: + \: 18x = \: 4140 }}$

$\quad {:} \longrightarrow \sf {\sf{ 23x = \: 4140 }}$

$\quad {:} \longrightarrow \sf {\sf{ x = \: \cancel \dfrac{4140}{23} }}$

$\quad {:} \longrightarrow \sf {\bf{ x = \: 108 }}$

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• Babita's share = x = Rs, 180
• Ahmed's share = 5x = 5 × 180 = Rs, 900
• Jhon's share = 1380 - 6x = 1380 - 6 × 180 = Rs, 300

$\bf \therefore \; Babita's\;share = Rs, 180$

$\bf \therefore \; Ahmed's\;share = Rs, 900$

$\bf \therefore \; Jhon's\;share = Rs, 300$

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Verification :-

$\quad {:} \longrightarrow \sf \boxed{\bf{Sum \: of \: all \: the \: Shares \: = \: 1380 }}$

$\quad {:} \longrightarrow \sf {\sf{ 180 \: + \: 900 \: +\: 300\: = \: 1380}}$

$\quad {:} \longrightarrow \sf {\tt{ 1380\: = \: 1380}}$

Hence, Proved

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Answer 2

Step-by-step explanation:

$\huge{\underline{\mathrm{Question}}}$

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Divide Rs,1380 among Ahmed, John, Babita so that amount Ahmed receives is 5 times as much as Babita's share and is 3 times as much as John's share.

$\huge{\underline{\mathrm{Answer}}}$

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∴ Let babita's share be x

∴ Then Ahmed's share be = 5 x

∴ John's share = Total Amount -( babita's share + Ahmed's share )

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$\: \: ⇒ \: Rs.\: 1380 - (x \: + \: 5) = rupees \: (1380 - 6x)$

It is given that Ahmed's share is three times John's share.

$\: \: \: \:⇒5x = 3(1380 - 6x) \\ ⇒5x = 4140 - 18x \\ ⇒5x + 18x = 4140 \\ ⇒23x = 4140 \\ \\ ⇒x = \frac{4140}{23} = 180$

∴ Babita's share = Rs. 180

∴ Ahmed's share = Rs. ( 5 × 180 )

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⇒${\boxed{Rs. 900}}$

∴ John's share = Rs. ( 1380 - 6 × 180 )

⇒${\boxed{Rs. 300}}$

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