1.

A cricketer has a certain average for 12 innings. In the thirteenth inning, he scored 78 runs, thereby increasing his average by 5 runs. His new average is:1). 18 runs2). 52 runs3). 55 runs4). 60 runs

Answer»

We know that,

Average = (Sum of all quantities)/(Number of quantities)

Let INITIAL average = x

∴ x = (TOTAL runs scored in 12 innings)/12

Total runs scored in 12 innings = 12X

? He scored 78runs in 13th inning,

Total runs scored in 13 innings = 12x + 78

∴ New average = (12x + 78)/13

Since average increases by 5,

$(\therefore {\RM{\;x}} + 5 = \frac{{{\rm{\;}}12{\rm{x\;}} + 78}}{{13}})$

⇒ 13(x + 5) = 12x + 78

⇒ 13x + 65 = 12x + 78

⇒ x = 13

∴ New average = 13 + 5 = 18


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