Aditya is celebrating his birthday. He invited his friends. He bought a packet of
toffees/candies which contains 120 candies. He arranges the candies such that in the first row
there are 3 candies, in second there are 5 candies, in third there are 7 candies and so on.
(a) Find the total number of rows of candies.
(i) 12 (ii) 10 (iii) 14 (iv) 8
(b) How many candies are placed in last row?
(i) 22 (ii) 21 (iii) 24 (iv) 18
(c) Find the difference in number of candies placed in 7th and 3rd row.
(i) 8 (ii) 10 (iii) 12 (iv) 14
(d) If Aditya decides to make 15 rows, then how many total candies will be placed by him
with the same arrangement?
(i) 200 (ii) 150 (iii) 255 (iv) 210
(e) Find the number of candies in 12th row.
(i) 21 (ii) 30 (iii) 25 (iv) 19
Answers
Given : A pocket of toffees and candies. It contains 120 candies.
He arranges the candies such that in first row there are 3 candies, in second there are 5, in third there are 7 and so on.
To Find : total number rows of candies
Solution:
Candies in 1st row = 3
Candies in 2nd row = 5
Candies in 3rd row = 7
a = 3
d = 2
let say n rows
Sum = (n/2)(2a + ( n- 1)d) ≥ 120
=> (n/2)( 2(3) + (n - 1)2) ≥ 120
=> n (3 + n - 1) ≥ 120
=> n(n + 2) ≥ 120
10(12) = 120
=> n = 10
total number rows of candies will be = 10
Candies placed in last 10th row
= 3 + (10 - 1)2
= 21
difference in number of candies placed in 7th and 3rd row.
a + ( 7 - 1)d - (a + (3 - 1)d) = 4d = 4(2) = 8
Candies for 15 rows
= (15/2)(2*3 + (15 - 1)2)
= 15(3 + 14)
= 255
candies in 12th row.
3 + (12 - 1)2 = 25
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Step-by-step explanation:
c,a7-a3
=a+6d -a+2d
3+6×2-3+2×2
3+12-3+4
15-1
14 is the number of candy placed in 7th and 3rd row.