1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square such that each of its sides contains 8 balls less than each side of triangle had. The initial number of balls lies in the interval

A
(1510,1560)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(1520,1570)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(1530,1580)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(1550,1600)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C (1530,1580)Let there be n rows in a triangle ∴ Number of balls =n(n+1)2 and n(n+1)2+669=(n−8)2⇒n2+n+1338=2(n2−16n+64)⇒n2−33n−1210=0⇒n2−55n+22n−1210=0⇒(n−55)(n+22)=0⇒n=55 ∴ Number of initial balls =n(n+1)2=55×28=1540

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Arithmetic Progression
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program