Question

A multistorey building is constructed with stilt parking. There is a provision of lift, as well as staircase from the ground floor to the top floor. The number of stairs from the ground floor to the first floor is 10, from the first floor to the second floor is 24, from the second floor to the third floor is 38 and so on.

Based on the above information, answer the following questions:

1. Does 10, 24, 38, ... form an A.P.? Justify your answer.   [1]
2. What will be the total number of stairs from the ground floor to the eleventh floor?   [1]
3. A person supplies water cans to people living in the building. As water cans are heavy, he supplies water cans on each floor, carrying one at a time. He supplied the water can from the ground floor to the first floor, came back and supplied water can to the second floor, again came back then supplied water can to the third floor and so on.

1. Find the total number of stairs he climbed up and down to supply water till the sixth floor, using A.P.   [2]
   OR
2. The next day, following the same process, if a person climbed up and down a total of 380 stairs, till which floor did he supply water cans?   [2]

Answer 1

i. A.P. = 10, 24, 38, ...

d₁ = 24 – 10

= 14

d₂ = 38 – 24

= 14

d₁ = d₂

∴ Given terms are in A.P.

ii. a = 10, d = 14, n = 11

`S_n = n/2 [2a + (n - 1)d]`

`S_11 = 11/2 [2(10) + (11 - 1)14]`

= `11/2 [20 + 10 xx 14]`

= `11/2 [20 + 140]`

= `11/2 xx 160`

= 11 × 80

= 880 stairs

iii. a. For first floor, 10 stairs up and 10 stairs down

∴ Total = 20 = (2 × 10)

For 2^nd floor, 24 stairs up and 24 down

∴ Total = 2 × 24 = 48

∴ Total no. of stairs, he climbs up and down

Till 6^th floor = 2 × 5₆

= `2 xx 6/2 [2(10) + (6 - 1)14]`

= 6[20 + 70]

= 6 × 90

= 540

OR

iii. b. 2 × S_n = 380

`2 xx n/2 [2(10) + (n - 1)14] = 380`

n[20 + 14n – 14] = 380

n[14n + 6] = 380

14n² + 6n – 380 = 0

7n² + 3n – 190 = 0

7n² + 38n – 35n – 190 = 0

n(7n + 38) – 5(7n + 38) = 0

(7n + 38)(n – 5) = 0

7n + 38 = 0

`n = (-38)/7`

n – 5 = 0

n = 5   ...(Not possible)

∴ Till 5^th floor, he can supply water can.