Question

1.
Average weight of a group of 6 girls is 26. If we
replace a girl of weight 30 in the group with
another girl so that new average increases by 5.
Find the weight of new girl.​

Answer 1

Answer:

60 kg

Step-by-step explanation:

Average = sum/no.    of quantities

   In the question,

⇒ 26 = (sum of weight of 6 girls)/6

⇒ 26*6 = sum of weight of 6 girls

⇒ 156 = sum of weight of 6 girls

Let the weight of the new girl be x. When a girl of 30 kg is replaced, total weight gets reduced by 30 and increases by x. Average increases by 5 or 26 + 5 = 31.

Total weight(now) = 156 - 30 + x

                               = 126 + x

⇒ average = (126 + x)/6

⇒ 31 = (126 + x)/6

⇒ 186 = 126 + x

⇒ 60 = x

Answer 2

Given : Average weight of a group of 6 girls is 26 & we replace a girl of weight 30 in the group with another girl so that new average increases by 5.

Exigency to find : The weight of new girl.

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⠀⠀⠀⠀Finding Sum of Weight of 6 girls :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Average \:: \dfrac{Sum\:of\:Weight \:of\:no.\:of\:girls\:}{No.\:of\:girls\:}}\bigg\rgroup$

⠀⠀⠀⠀Here Average is the 26 & No. of Girls is 6 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf 26 = \dfrac{Sum\:of\:Weight \:of\:6\:girls\:}{6}$

$\qquad \longmapsto \sf 26 \times 6 = Sum\:of\:Weight \:of\:6\:\:girls\:$

$\qquad \longmapsto \frak{\underline{\purple{\:Sum\:of\:Weight \:of\:6.\:\:girls\: = 156 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Sum\:of\:Weight \:of\:6\:girls\: \:is\:\bf{156\:}}}}$

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⠀⠀⠀⠀Finding Weight of New Girl :

❍ Let's Consider Weight of New Girl be x .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: To\: \: the \: Given \: Question \::}}$

━━━ We replace a girl of weight 30 in the group with another girl so that new average increases by 5.

$\qquad \longmapsto \sf Average + 5 = \dfrac{Sum\:of\:Weight \:of\:6\:girls\:- 30+ \:x }{No.\:of\:Girls}$

$\qquad \longmapsto \sf 26 + 5 = \dfrac{ 156 - 30 + x }{6}$

$\qquad \longmapsto \sf 31 = \dfrac{ 156 - 30 + x }{6}$

$\qquad \longmapsto \sf 31 = \dfrac{ 126 + x }{6}$

$\qquad \longmapsto \sf 31 \times 6 = 126 + x$

$\qquad \longmapsto \sf 18 6 = 126 + x$

$\qquad \longmapsto \sf 18 6 - 126 = x$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 60 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Weight \:of\:New \:girl\:is\:\bf{60}}}}$

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