If $m:n=3:8$, find the value of $\left( 3m+2n \right):\left( 5m+n \right)$ - Noon Academy

If $m:n=3:8$ , find the value of $\left( 3m+2n \right):\left( 5m+n \right)$

Class 10 | Frank | ICSE | Maths | Ratio and Proportion

If $m:n=3:8$ , find the value of $\left( 3m+2n \right):\left( 5m+n \right)$

The ratio is used for comparing two quantities of the sane kind.

The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion.

The concept of ratio and proportion is majorly based on ratios and fractions.

Solution:

From the question it is given that,

$m:n=3:8$

$m/n=3/8$

$\left( 3m+2n \right)/\left( 5m/n \right)$

Now, divide both numerator and denominator by $'n'$ we get,

$=\left[ \left( 3m/n \right)+\left( 2n/n \right) \right]/\left[ \left( 5m/n \right)+\left( n/n \right) \right]$

$=\left[ \left( 3m/n \right)+2 \right]/\left[ \left( 5m/n \right)+1 \right]$

Now, substitute the value of m and n we get,

$=\left[ \left( 3\left( 3/8 \right) \right)+2 \right]/\left[ \left( 5\left( 3/8 \right) \right)+1 \right]$

$=\left( \left( 9/8 \right)+2 \right)/\left( \left( 15/8 \right)+1 \right)$

$=25/23$

Therefore, the value of $\left( 3m+2n \right):\left( 5m+n \right)=25:23$

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