Question

a shopkeeper has some pens out of which 1/3rd are blue , 1/4th are black and the remaining are green . If he has 10 green pens, how many does he have in total.​

Answer 1

Answer:

∴ The shopkeeper has $33$ pens.        

Step-by-step explanation:

• In context with question asked,
• We have to find total number of pens.
• Let, $x$ be the total number of pens.
• It is given that, number of blue pens = $10$

      Number of blue pens = $\frac{x}{3}$

      Number of black pen = $\frac{x}{4}$

• Now, according to given condition, the equation becomes,

  Total number of pens = Number of blue pen + black pens + green pens

                           ∴ $x=\frac{x}{3} +\frac{x}{4} +10$

• LCM of $3,4$ and $1$ is $12$.    
• Equating the denominators, we get

                         ∴ $x=\frac{x\times4}{4\times3} +\frac{x\times 3}{4\times3} +\frac{10\times12}{1\times12}$

                         ∴ $x=\frac{4x}{12} +\frac{3x}{12} +\frac{120}{12}$

                         ∴ $x=\frac{4x+3x+120}{12}$

                      ∴ $x\times 12=7x+120$

                   ∴ $12x-7x=120$      

                           ∴ $5x=120$

                             ∴ $x=\frac{120}{5}$

                             ∴ $x=24$    

• ∴ Number of blue pens = $\frac{24}{3}$ = $8$ pens

         Number of blue pens = $\frac{24}{4}=6$ pens

• ∴ The shopkeeper has $24$ pens.              

  

Answer 2

Shopkeeper has 24 pens in Total if  1/3rd are blue , 1/4th are black and the remaining 10 are green

Given:

• A shopkeeper has some pens
• 1/3rd are blue
• 1/4th are black
• remaining 10 pens are green

To Find:

• Total number of pens

Solution:

Step 1:

Assume that shopkeeper has 12x pens

Step 2:

Calculate the number of blue pens

= (1/3)12x

= 4x

Step 3:

Calculate the number of black pens

= (1/4)12x

=3x

Step 4:

Add black , blue and green pens and equate with total pens to solve for x

4x + 3x + 10 = 12x

=> 7x + 10 = 12

=> 10 = 5x

=>  2 = x

Step 5:

Use x = 2 and calculate 12x

12x = 12(2) = 24

Shopkeeper has 24 pens in Total