Question

A sum of many is divided in the ratio 2:3:7 if the largest share is 112calcate the smallest share

Answer 1

Let the ratio be x
Then do it as follows
Then x will not be the answer
You have to put it back on the ratio

Answer 2

$\pink\bigstar$Answer:

• The smallest share is 32

$\blue\bigstar$Given:

• The sum of some numbers is divided in the ratio 2 : 3 : 7.
• The largest share is 112.

$\red\bigstar$To find:

• The value of smallest share.

$\green\bigstar$ Solution:

Let all the shares in terms of x.

Given ratio -

• 2 : 3 : 7

$\therefore$ the shares are 2x , 3x and 7x

It is also given that the largest share is 112. The largest share among 2x , 3x and 7x is 7x.

$\therefore$ 7x = 112

Now by solving the equation, we get :

7x = 112

$\implies$ x = $\sf \dfrac{112}{7}$

$\implies$$\boxed{\sf x \:= \:16\:}$

Now, the value of all shares:

$\hookrightarrow$ 2x

= 2 × 16

= 32

_________

$\hookrightarrow$ 3x

= 3 × 16

= 48

_________

$\hookrightarrow$ 7x

= 112

[Given]

$\therefore$ the value of smallest share is 32

$\pink\bigstar$ Concepts Used:

• Assumption of shares in terms of x
• Equation of the variable with the given value
• Finding out the value of shares by multiplication

$\blue\bigstar$Extra - Information:

• When a fraction is represented in the form of a : b, then it is a ratio.
• The ratio is the number which can be used to express one quantity as a fraction of the other ones.
• The two numbers in a ratio can only be compared when they have the same unit.
• We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’
• The ratio should exist between the quantities of the same kind.
• While comparing two things, the units should be similar.
• There should be significant order of terms.
• The comparison of two ratios can be performed, if the ratios are equivalent like the fractions