During the sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both and same number of pencils and crayons, how many of each would you need to buy?
Last updated date: 22nd Mar 2023
•
Total views: 308.7k
•
Views today: 8.87k
Answer
308.7k+ views
Hint- In order to find the same number of crayons and pencils, try to solve using L.C.M.
Number of colour pencils to be packed in a packet \[ = 24\]
Number of crayons to be packed in a packet \[ = 32\]
We have to find the L.C.M of $24$ and $32$.
\[
24 = 2 \times 2 \times 3 \\
32 = 2 \times 2 \times 2 \times 2 \times 2 \\
\]
L.C.M of $24$ and $ 32 $ \[{\text{ = }}2 \times 2 \times 2 \times 2 \times 2 \times 3 = 96\]
Capacity of $1$ packet of colour pencils \[ = 24\]
So, for 96 pencils, number of packets needed \[ = \dfrac{{96}}{{24}} = 4\]
$3$Now, capacity of $1$ packet of crayons \[ = 32\]
SO, for 96 crayons, number of packets needed \[ = \dfrac{{96}}{{32}} = 3\]
$\therefore $ In order to buy full packs of both and same number of pencils and crayons, we need to buy $4$ packets of colour pencils and $3$ packets of crayons.
Note- L.C.M stands for Lowest Common Multiple. For any two numbers a and b, L.C.M is the smallest positive integer that is divided by both a and b. Hence, whenever you see problems like these, L.C.M is the shortest way to find solutions.
Number of colour pencils to be packed in a packet \[ = 24\]
Number of crayons to be packed in a packet \[ = 32\]
We have to find the L.C.M of $24$ and $32$.
\[
24 = 2 \times 2 \times 3 \\
32 = 2 \times 2 \times 2 \times 2 \times 2 \\
\]
L.C.M of $24$ and $ 32 $ \[{\text{ = }}2 \times 2 \times 2 \times 2 \times 2 \times 3 = 96\]
Capacity of $1$ packet of colour pencils \[ = 24\]
So, for 96 pencils, number of packets needed \[ = \dfrac{{96}}{{24}} = 4\]
$3$Now, capacity of $1$ packet of crayons \[ = 32\]
SO, for 96 crayons, number of packets needed \[ = \dfrac{{96}}{{32}} = 3\]
$\therefore $ In order to buy full packs of both and same number of pencils and crayons, we need to buy $4$ packets of colour pencils and $3$ packets of crayons.
Note- L.C.M stands for Lowest Common Multiple. For any two numbers a and b, L.C.M is the smallest positive integer that is divided by both a and b. Hence, whenever you see problems like these, L.C.M is the shortest way to find solutions.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Name the Largest and the Smallest Cell in the Human Body ?

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

Lysosomes are known as suicidal bags of cell why class 11 biology CBSE

Two balls are dropped from different heights at different class 11 physics CBSE

A 30 solution of H2O2 is marketed as 100 volume hydrogen class 11 chemistry JEE_Main

A sample of an ideal gas is expanded from 1dm3 to 3dm3 class 11 chemistry CBSE
