Question

The average marks obtained by 5 students in a group is 226. If the marks obtained by
four of them 180, 281, 279, 200. Find the marks obtained by the 5th student.

Answer 1

Given:

• The average marks obtained by 5 students is 226.
• The marks obtained by four of them are 180, 281, 279 and 200.

To find:

• The marks obtained by the 5th student.

Formula used:

• $\sf{Average=\dfrac{Sum\:of\:terms}{No.of.terms}}$

Solution:

The average marks of 5 students is given and the marks of 4 students are given. We need to calculate the marks of the 5th student.

Let the marks of the 5th student be $\rm{z}$.

$\longmapsto{\sf{Average=\dfrac{Sum\:of\:terms}{No.of.terms}}}$

• Here, the number of terms is 5, as there are 5 students.

On substituting the values,

$\\ \longmapsto\sf Average = \dfrac{Sum \: of \: terms}{Number \: of \: terms} \\ \\ \\ \longmapsto{\sf{226=\dfrac{180+281+279+200+z}{5}}} \\ \\ \sf \longmapsto{226 = \dfrac{461 + 479 + z}{5}} \\ \\ \sf \longmapsto 226= \dfrac{940 + z}{ 5} \\ \\ \longmapsto \sf 226 \times 5 = 940 + z \\ \\ \longmapsto \sf 1130 = 940 + z \\ \\ \longmapsto \sf 1130 - 940 = z \\ \\ \longmapsto { \boxed{\frak{ \red{190}}}} \: \sf = z$

$\:$

Verification:

Substituting 190 in place of z in the formula:

$\\ \longmapsto\sf Average = \dfrac{Sum \: of \: terms}{Number \: of \: terms} \\ \\ \\ \longmapsto{\sf{226=\dfrac{180+281+279+200+190}{5}}} \\ \\ \sf \longmapsto{226 = \dfrac{461 + 479 + 190}{5}} \\ \\ \sf \longmapsto 226= \dfrac{940 + 190}{ 5} \\ \\ \longmapsto \sf 226 = \dfrac{ \cancel{1130}}{ \cancel{5}} \\ \\ \longmapsto \sf 226 = 226 \\ \\ \longmapsto \sf L.H.S. = R.H.S.$

$\\ \therefore\underline{\sf{The\: marks\:obtained\:by\:the\:5^{th}\: student\:is\:\textsf{\textbf{\purple{190}}}\sf{.}}}$

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