In a classroom, the average height of all the boys was 170 cm. Rahim recently…
2025
In a classroom, the average height of all the boys was 170 cm. Rahim recently joined the class, which originally had 20 boys, increasing the average height to 171 cm. Find the height of Rahim.
- A.
171
- B.
181
- C.
191
- D.
201
Show answer & explanation
Correct answer: C
Concept: when a new member joins a group and changes its average, the new member's value equals the new total minus the original total. Equivalently, New member's value = New average + (Original count × Increase in average).
Original total height of 20 boys = 20 × 170 = 3400 cm.
After Rahim joins, the class has 21 boys with a new average of 171 cm, so the new total height = 21 × 171 = 3591 cm.
Rahim's height = New total − Original total = 3591 − 3400 = 191 cm.
Cross-check using the shortcut identity: Rahim's height = New average + (Original count × Increase in average) = 171 + (20 × 1) = 191 cm — confirming the result.