Selection Post Phase XIV (10th)23 Sep 2026Shift 3Average

The average of the six numbers 52, 71, 43, 22, a and b is 55. The average of the seven numbers 42, 45, 49, 51, 42, c and d is 53. Find the average of a, b, c and d.

छह संख्याओं 52, 71, 43, 22, a और b का औसत (Average) 55 है। सात संख्याओं 42, 45, 49, 51, 42, c और d का औसत 53 है। a, b, c और d का औसत ज्ञात कीजिए।

Answer और ExplanationAnswer and explanation

Answer: (A) 71

छह संख्याओं का योग (Sum) = 6 × 55 = 330
52 + 71 + 43 + 22 = 188 ⇒ a + b = 330 − 188 = 142
सात संख्याओं का योग = 7 × 53 = 371
42 + 45 + 49 + 51 + 42 = 229 ⇒ c + d = 371 − 229 = 142
a, b, c, d का औसत (Average) = 142 + 1424 = 2844 = 71
✓
अभीष्ट औसत 71 है।
Total of the six numbers = 6 × 55 = 330
52 + 71 + 43 + 22 = 188 ⇒ a + b = 330 − 188 = 142
Total of the seven numbers = 7 × 53 = 371
42 + 45 + 49 + 51 + 42 = 229 ⇒ c + d = 371 − 229 = 142
Average of a, b, c, d = 142 + 1424 = 2844 = 71
✓
The required average is 71.
SMART APPROACH

विचलन (Deviation) से करें। पहले समूह में 55 से: −3 + 16 − 12 − 33 = −32, तो a + b = 2 × 55 + 32 = 142। दूसरे समूह में 53 से: −11 − 8 − 4 − 2 − 11 = −36, तो c + d = 2 × 53 + 36 = 142। औसत (Average) = 2844 = 71।

Work with deviations. First set from 55: −3 + 16 − 12 − 33 = −32, so a + b = 2 × 55 + 32 = 142. Second set from 53: −11 − 8 − 4 − 2 − 11 = −36, so c + d = 2 × 53 + 36 = 142. Average = 2844 = 71.

Source: Selection Post Phase XIV (10th) · 23 Sep 2026 · Shift 3। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (10th) · 23 Sep 2026 · Shift 3. Solution by Prashant Sir, from Vijayastra.