Question

perations on Whole NumbersT2(d) Three measuring tapes are 10, 15 and 25 m long. Find the shortest lengthwhich can be measured exactly by any one of these tapes. Som(e) Asick person has to take three types of medicines. He takes type-X in every3 hours, type-Y in every 4 hours and type-Z in every 6 hours. If he takes atypes of medicine at the same time at 6 a.m., at what time does he take athese types again at a time? 6pm(f) A book, a pen and a box cost Rs 36, Rs 45 and Rs 54 respectively. Find thesmallest sum of money with which the exact number of books, pens anboxes can be purchased. 120

Answer 1

(f) To find the smallest amount of money that would allow us to purchase an exact amount of any item, we need to find the Least Commom Multiple of the three values.

The first step is to factorate the numbers in their prime factors:

`\begin{gathered} 36=2\cdot2\cdot3\cdot3 \\ 45=3\cdot3\cdot5 \\ 54=2\cdot3\cdot3\cdot3 \end{gathered}`

Then, we pick the maximum number of times that each prime factors show up and create a new number:

`\begin{gathered} \text{number 2: 2 times} \\ \text{number 3: 3 times} \\ \text{number 5: 1 time} \\ \text{new number: 2}\cdot2\cdot3\cdot3\cdot3\cdot5=540 \end{gathered}`

So the smallest amount of money to purchase an exact number of any item is Rs 540