Question

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

Answer 1

• (a) 10, (b) 21, (c) 8, (d) 255, (e) 25

Explanation:

(a)Total number of candies = 120

The number of candies in the rows form AP sequence:

• 3, 5, 7, ...

The first term is a=3 and common difference is d=2

Sum of n terms:

• S = 1/2n(2a + (n - 1)d)

Substitute values and solve for n:

• 120 = 1/2n(2*3 + 2(n - 1))
• 120 = 3n + n² - n
• n² + 2n = 120
• n²+ 2n + 1 = 121
• (n + 1)² = 121
• n + 1 = 11
• n = 10

Correct choice is (ii) 10

(b) Formula for nth term:

• a(n) = a + (n - 1)d
• a(10) = 3 + 9*2 = 3 + 18 = 21 candies

Correct choice is (ii) 21

(c) Use same formula:

• a(7) - a(3) = a + 6d - a - 2d = 4d
• 4d = 4*2 = 8

Correct choice is (i) 8

(d) Sum of candies in 15 rows

• S(15) = 1/2(15)(2*3 + (15 - 1)*2) = 1/2(15)(6 + 28) = 255

Correct choice is (iii) 255

(e) Number of candies in 12th row:

• a(12) = 3 + (12 - 1)*2 = 3 + 22 = 25

Correct choice is (iii) 25