Meera’s mother start a new shoe shop. To display the shoes ,she put 3 pairs of shoes in 1st row,5pairs in 2nd row ,7 pairs in 3rd row and so on On the basis of above information, answer the following Questions i) If she put a total of 120 pairs of shoes, then the number of rows required are .. a) 5 b) 6 c) 7 d) 10 ii) Difference of pairs of shoes in 17th row and 10th row is a) 7 b) 14 c) 21 d) 28 iii) On the next day, she arranges x pairs of shoes in 15 th row, then x is a) 21 b) 26 c) 31 d) 42 iv) Find the pairs of shoes in 30th row a) 61 b) 67 c) 56 d)59 v) The total number of shoes in 5th & 8th row is a) 7 b) 14 c) 28 d) 56
Answers
Answer:
(i) Option (d) 10 is the correct option.
(ii) Option (b) 14 is the correct option.
(iii) Option (c) 31 is the correct option.
(iv) Option (a) 61 is the correct option.
(v) Option (c) 28 is the correct option.
Step-by-step explanation:
The given data form an AP (3, 5, 7, . . . . )
(i) We need to find the number of rows for 120 pair of shoes.
We know that
and that aₙ = a + (n - 1) d
where Sₙ = sum of n terms
n = number of terms of the AP
a = first term of the AP
d = common difference of the AP
aₙ = nth term of the AP
On substitution,
=> 120 =
=> 120 =
=> 240 = n [4 + 2n]
=> 240 = 4n + 2n²
=> 120 = 2n + n²
=> n² + 2n - 120 = 0
=> n² + 12n - 10n - 120 = 0
=> n(n + 12) -10 (n + 12) = 0
=> (n + 12) (n - 10) = 0
=> n + 12 = 0 or n - 10 = 0
=> n = -12 or n = 10
As the number of rows cannot be negative, n = 10
Therefore, 10 rows will be required to put 120 pair of shoes.
Therefore, Option (d) 10 is the correct option.
(ii) Difference of pairs of shoes in 17th row and 10th row
= 17th term of the AP - 10th term of the AP
= [ 3 + (17 - 1) 2 ] - [ 3 + (10 - 1) 2]
= [ 3 + 16* 2 ] - [ 3 + 9* 2]
= [ 3 + 32 ] - [ 3 + 18]
= 35 - 21
= 14
Therefore, the difference of pairs of shoes in 17th row and 10th row is 14
Therefore, Option (b) 14 is the correct option.
(iii) Number of pairs in the 15th row = 3 + (15 - 1) 2
= 3 + 14 * 2
= 3 + 28
= 31
Therefore, there are 31 pairs of shoes in the 15th row.
Therefore, Option (c) 31 is the correct option.
(iv) Number of pairs in the 30th row = 3 + (30 - 1) 2
= 3 + 29 * 2
= 3 + 58
= 61
Therefore, there are 61 pairs of shoes in the 30th row.
Therefore, Option (a) 61 is the correct option.
(v) Total number of shoes in the 5th and the 8th row
= Shoes in the 5th row + Shoes in the 8th row
= 5th term of the AP + 8th term of the AP
= [ 3 + (5 - 1) 2 ] + [ 3 + (8 - 1) 2]
= [ 3 + 4* 2 ] + [ 3 + 7* 2]
= [ 3 + 8 ] + [ 3 + 14]
= 11 + 17
= 28
Therefore, the total number of shoes in the 5th and the 8th row is 28
Therefore, Option (c) 28 is the correct option.
Answer:
i) 10
ii)14
I was only able to do this much hope it helps
