Question

6. Raghu bought some pencils and pens. Pencils were 35 more than the pens. If the ratio of the
pencils to the pens was 8:3, how many of each type did he buy? 56, 21​

Answer 1

Given :

• Number of pencils = 35
• Ratio of pencils to pens us 8:3

To calculate :

• How many each type did he bought.

Calculation :

Assumption: Let us assume the number of pencils as 8x and number of pens as 3x.

Here, we need to subtract 3x from 8x in order to find the separate results of number of pens and pencils.

$: \implies \rm 8x - 3x \\ \\ : \:\implies \rm 5x$

Given that,

• Pencils were 35 more than pens.

Now, let's calculate the value of x by dividing 35 by 5.

$: \implies \rm x = \cancel \dfrac{35}{5}$

On dividing the numbers,

$: \implies \underline{ \boxed{ \rm x = 7}} \green{ \bigstar}$

Thus, the value of x is 7.

$\purple{\dag}$According to the Question:

Now, let's calculate the total number of pencils and pens.

For this, we simply need to multiplying the ratios of pencils & pens with the value of x.

$: \implies \rm \underbrace{8}_{(Pencils)} : \underbrace{3}_{(Pens)}$

$\dag \: \underline{\underline{ \sf{Total \: number \: of \: pencils: }}}$

Multiplying 8 with 7,

$: \implies \rm Number \: of \: pencils = 8 \times 7$

On performing multiplication,

$: \implies \underline{ \boxed{ \pink{\rm{No. \: of \: pencils = 56}}} }$

$\dag \: \underline{\underline{ \sf{Total \: number \: of \: pens: }}}$

Multiplying 3 with 7,

$: \implies \rm Number \: of \: pens = 3 \times 7$

On performing multiplication,

$: \implies \underline{ \boxed{ \pink{\rm{No. \: of \: pens = 21}}} }$

Therefore, the total number of pencils is 56 pencils and total number of pens is 21 pencils.

Answer 2

Solution:-

❍ Let the pencils be 35 + x and pen be x respectively.

$\\ \underline{\bigstar\boldsymbol{According \;to\;the\;Question:}}$

• Here,The ratio of pencils to the pen was 8:3 and pencils were 35 more than the pens.So we can divide pencils by pens with given ratio.So that we will find the number of pens and number of pencils.

Let's do it,

_________________________________

$\\ \implies \: \sf{ \frac{35 + x}{x} = \frac{8}{3}} \\ \\ \implies \: \sf{(35 + x)3} = (x)8 \\ \\ \implies \: \sf{105 + 3x = 8x} \\ \\ \implies \: \sf{105 = 8x - 3x} \\ \\ \implies \: \sf{105 = 5x} \\ \\ \implies \: \sf{ x = \cancel{\frac{105}{5}}} \\ \\ \implies \: \underline {\boxed{\frak{x = 21}}} \: \pink{ \bigstar}$

Hence,

• The number of pens = 21.
• The number of pencils = 35 + 21 = 56.