UPSC CDS 2 2022 Math Paper

Average = Sum of observations/Number of observations
According to the question
⇒ (60 × 60 + 50 × 80 + 50 × 40 + x × 50)/(60 + 50 + 50 + x) = 58
⇒ (3600 + 4000 + 2000 + 50x)/(160 + x) = 58
⇒ (9600 + 50x)/160 + x) = 58
⇒ 9600 + 50x = 9280 + 58x
⇒ (58x − 50x) = (9600 − 9280)
⇒ 8x = 320
⇒ x = 40