For the least number of tiles, the size of the ltie must be the maximum.
Maximum size of the tile = HCF of 1517 cm and 902 cm = 41 cm.
Hence, required number of tiles
= Area of cellingArea of each tile=(1517×90241×41)=814$$\begin{array}{rl}& \text{=}\frac{\text{Area of celling}}{\text{Area of each tile}}\\ & =\left(\frac{1517\times 902}{41\times 41}\right)\\ & =814\end{array}$$
For the least number of tiles, the size of the ltie must be the maximum.
Maximum size of the tile = HCF of 1517 cm and 902 cm = 41 cm.
Hence, required number of tiles
= Area of cellingArea of each tile=(1517×90241×41)=814$$\begin{array}{rl}& \text{=}\frac{\text{Area of celling}}{\text{Area of each tile}}\\ & =\left(\frac{1517\times 902}{41\times 41}\right)\\ & =814\end{array}$$
For the least number of bottles, the capacity of each bottle must be maximum.
Capacity of each bottle = HCF of 403 litres, 465 litres and 496 litres = 31 litres.
Hence,
required number of bottles
LCM of left(24, 36, 54)
⇒ 12 × 2 × 3 × 3 = 216 sec
⇒ They will change simultaneously after every 216 seconds
⇒ ^{216}/_{60} ⇒ 3^{36}/_{60} ⇒ 3 minute 36 seconds
⇒ They change 1^{st} at 10:15:00 AM
So, again they change at = 10:18:36 AM
= Here 4 is common factor (common factor is the HCF of the given number
∴ HCF = 4
So, for the given numbers the HCF should be multiple of 4
⇒ Hence go through options which is not a multiple of 4 is 35
Hence answer is 35