Suresh scores an aggregate of 64%, scoring an average of 60% in 4 subjects and 72% in others. If all the tests were of equal marks, in total there were how many subjects?
Suresh scores an aggregate of 64%, scoring an average of 60% in 4 subjects and 72% in others. If all the tests were of equal marks, in total there were how many subjects?
1). 2
2). 4
3). 5
4). 6
1 answers
We know that, average = Sum of all quantities/Number of quantities
∴ Average marks = Sum of marks in all subjects/Number of subjects
? Average of 4 subjects is 60%,
60 = Sum of marks of 4 subjects/4
⇒ Sum of marks of 4 subjects = 60 × 4 = 240
Let the number of remaining subjects be x
? Average of x subjects is 72%,
72 = Sum of marks in x subjects/x
⇒ Sum of marks in x subjects = 72x
Total number of subjects = x + 4
∴ Total marks obtained in (x + 4) subjects = 240 + 72x
? Average of (x + 4) subjects is 64%,
$(64\; = \frac{{240\; + \;72x}}{{x\; + \;4}})$
⇒ 64 × (x + 4) = 240 + 72x
⇒ 64x + 256 = 240 + 72x
⇒ 8x = 16
⇒ x = 2
∴ Number of remaining subjects = 2
⇒ Total no. of subjects = 4 + 2 = 6