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.
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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.
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
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 :
[tex]\dag\:\:\it{ As,\:We\:know\:that\::}\\[/tex]
[tex]\qquad \dag\:\:\bigg\lgroup \sf{ Average \:: \dfrac{Sum\:of\:Weight \:of\:no.\:of\:girls\:}{No.\:of\:girls\:}}\bigg\rgroup \\\\[/tex]
⠀⠀⠀⠀Here Average is the 26 & No. of Girls is 6 .
⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]
[tex]\qquad \longmapsto \sf 26 = \dfrac{Sum\:of\:Weight \:of\:6\:girls\:}{6}\\\\[/tex]
[tex]\qquad \longmapsto \sf 26 \times 6 = Sum\:of\:Weight \:of\:6\:\:girls\:\\\\[/tex]
[tex]\qquad \longmapsto \frak{\underline{\purple{\:Sum\:of\:Weight \:of\:6.\:\:girls\: = 156 }} }\bigstar \\[/tex]
Therefore,
⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm {\:Sum\:of\:Weight \:of\:6\:girls\: \:is\:\bf{156\:}}}}\\[/tex]
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⠀⠀⠀⠀Finding Weight of New Girl :
❍ Let’s Consider Weight of New Girl be x .
⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:According \: To\: \: the \: Given \: Question \::}}\\[/tex]
━━━ We replace a girl of weight 30 in the group with another girl so that new average increases by 5.
[tex]\qquad \longmapsto \sf Average + 5 = \dfrac{Sum\:of\:Weight \:of\:6\:girls\:- 30+ \:x }{No.\:of\:Girls}\\\\[/tex]
[tex]\qquad \longmapsto \sf 26 + 5 = \dfrac{ 156 – 30 + x }{6} \\\\ [/tex]
[tex]\qquad \longmapsto \sf 31 = \dfrac{ 156 – 30 + x }{6} \\\\ [/tex]
[tex]\qquad \longmapsto \sf 31 = \dfrac{ 126 + x }{6} \\\\ [/tex]
[tex]\qquad \longmapsto \sf 31 \times 6 = 126 + x \\\\ [/tex]
[tex]\qquad \longmapsto \sf 18 6 = 126 + x \\\\ [/tex]
[tex]\qquad \longmapsto \sf 18 6 – 126 = x \\\\ [/tex]
[tex]\qquad \longmapsto \frak{\underline{\purple{\:x = 60 }} }\bigstar \\[/tex]
Therefore,
⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm {\:Weight \:of\:New \:girl\:is\:\bf{60}}}}\\[/tex]
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