Question

70) Average of the runs of 133 players of a team is 38. If the average of the runs of the male players is 43 and the
average of the runs of the female players is 24, then what will be the ratio of the total runs of male players and
the total runs of female players respectively ?​

Answer 1

Answer:

Given -

• Average of runs of 133 players of a team = 38
• The average of the runs of the male = 43
• The average of the runs of the female = 24

To find -

• The ratio of the total runs of male players and total runs of female players.

Solution -

$\\ \large \sf{ \underline{ \: \dag \: \: Sum \: \: of \: \: the \: \: total \: \: runs \: \: of \: \: the \: \: team \: - }}$

→ Number of players × average runs

→ 38 × 133

→ 5054

Now,

Let the total number of the male be M and total number of females be F.

Total runs scored by male and female = 43M + 24F.

1. 43 M + 24F = 5054
2. M + F = 133 => M= (F-133)

Now, by substituting M = F - 133 in equation 1, we obtain -

$\\ \sf \implies \: 43 (133 - F) + 24F = 5054 \\ \\ \\ \implies \sf \: 5719 - 43F \: + 24F = 5054 \\ \\ \\ \sf \underline{ by \: \: rearranging \: - } \\ \\ \\ \implies \sf \: 43F - 24F = 5719 - 5054 \\ \\ \\ \implies \sf \: 19F = 665 \\ \\ \\ \implies \sf \: F = \frac{665}{19} \\ \\ \\ \implies \sf \blue{F = 35}$

Male -

• 133 - 35 = 98

Ratio of both -

$\\ \implies \sf \: \frac{ (98 × 43)}{(35 × 24) } \\ \\ \\ \implies \large{ \boxed{ \sf{ \: \frac{301}{60} }}} \\ \\ \\ \Large{ \underline{ \bf { \: \star \: \: Required \: \: ratio = 301 \ratio \: 60}}}$

Answer 2

Answer:

REQUIRED RATIO:

301:60.