Divide ₹ 1100 among A, B, C so that A shall receive 3/7 of what B and C together receive and B may receive 2/9 of what A and C rec

2 thoughts on “Divide ₹ 1100 among A, B, C so that A shall receive 3/7 of what B and C together receive and B may receive 2/9 of what A and C rec”

1. Answer :

   Given that x+y+z 1100… (1)

   Given that x+y+z 1100… (1)Also given that,

   x = 3/7 (y +z)

   (y +z)y+z= 7x /3

   U sing (1) , we get x+ 7x /3 = 1100

   110010 /3 = 1100

   x = 1100 X 3 / 10 = Rs.330

   Rs.330Given that, y =2/3 (x+z)

   x+z =9y / 2

   U sing (1) we get, y + 9y / 2 = 1100

   11 y / 2 = 110

   y= Rs.200

   y= Rs.200now, using (1)

   y= Rs.200now, using (1)We get 330 + 200 +z = 1100

   y= Rs.200now, using (1)We get 330 + 200 +z = 1100530 + z = 1100

   y= Rs.200now, using (1)We get 330 + 200 +z = 1100530 + z = 1100 z = 1100 – 530 = 570

   hope it helps you ....

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2. Given:

   • Divide ₹ 1100 among A, B, C

   So that,

   ➛ A shall receive 3/7 of what B and C together receive.

   ➛ B may receive 2/9 of what A and C receive.

   To Find:

   • What is the share of each person ( A , B , C )

   Solution:

   ❍ Now, Let’s Assume that ,

   • ↦ Share of A = x

   • ↦ Share of B = y

   • ↦ Share of C = z

   [tex] \\ [/tex]

   ❍ As per the condition we get,

   [tex] \\ [/tex]

   ➛ X + Y + Z = 1100

   [tex] \\ [/tex]

   [tex]{ \underline{ \frak{As \: we \: know \: that}}}[/tex]

   • [tex]\tt \: x = \frac{3}{7} \times (y + z)[/tex]

   [tex] \\ [/tex]

   Which means,

   • [tex] \tt \: y + z = \frac{7x}{3} [/tex]

   [tex] \\ [/tex]

   [tex]{ \underline{ \frak{Now, putting \: the \: values \: in \: the \: first \: condition \: we \: get, }}}[/tex]

   [tex]{ : \implies} \sf \: x + \frac{7x}{3} = 1100 \: \\ \\ \\ { : \implies} \sf \frac{3x}{3} + \frac{7x}{3} = 1100 \\ \\ \\ { : \implies} \sf \frac{3x + 7x}{3} = 1100 \\ \\ \\ { : \implies} \sf \frac{10x}{3} = 1100 \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf x = \frac{110 \cancel0 \times 3}{1 \cancel0} \: \: \: \\ \\ \\ { : \implies} \sf x = 110 \times 3 \: \: \: \: \: \\ \\ \\ { : \implies} \sf { \pink{ \underline{ \boxed{ \frak {x = 330}}}}} \pink \bigstar \: \: \: \: \: \: [/tex]

   [tex] \\ [/tex]

   Henceforth ,

   [tex] \: \: \: \: \: \: \: { \underline{ \rm{The \: share \: of \: person \: A \: is \: rupees \: 330}}}[/tex]

   [tex] \\ [/tex]

   [tex]{ \underline{ \frak{ \dag \: As \: given \: that}}}[/tex]

   • [tex] \tt \: y \: = \frac{2}{9} (x + z)[/tex]

   [tex] \\ [/tex]

   So,

   • [tex] \tt \: x + z = \frac{9y}{2} [/tex]

   [tex] \\ [/tex]

   [tex]{ \underline{ \frak{Now, putting \: the \: values \: in \: the \: first \: condition \: we \: get, }}}[/tex]

   [tex] { : \implies}\sf \frac{9y}{2} + y = 1100 \: \: \: \\ \\ \\ { : \implies} \sf \frac{9y}{2} + \frac{2y}{2} = 1100 \: \\ \\ \\ { : \implies}\sf \frac{9y + 2y}{2} = 1100 \\ \\ \\ { : \implies}\sf \frac{11y}{2} = 1100 \: \: \: \: \: \\ \\ \\ { : \implies}\sf y = \frac{1100 \times 2}{11} \: \: \\ \\ \\ { : \implies}\sf{ \pink{ \underline{ \boxed{ \frak{y = 200}}}}} \pink \bigstar\: \: \: \: \: \: [/tex]

   [tex] \\ [/tex]

   Henceforth,

   [tex] \: \: \: \: \: \: \: \: \: { \underline{ \rm{The \: share \: of \: person \: b \: is \: rupees \: 200}}}[/tex]

   [tex] \\ [/tex]

   Now,

   [tex]{ \underline{ \frak{Now, putting \: the \: values \: of \: x \: and \: y \: in \: the \: equation \: we \: get}}}[/tex]

   [tex] { : \implies}\sf x + y + z = 1100 \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\sf 330 + 200 + z = 1100 \\ \\ \\ { : \implies}\sf 530 + z = 1100 \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\sf z = 1100 – 530 \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\sf { \pink{ \underline{ \boxed{ \frak{ z = 570}}}}} \pink \bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

   [tex] \\ [/tex]

   ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

   [tex] \: \: {\orange{ \underline{ \therefore{ \frak { The \: shares \: are \: 330,200,570 \: respectivly}}}}}[/tex]

   ⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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