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If a:b=4:7, find the following(i) \left( 5a+2b \right)/\left( 5a-2b \right)(ii) \left( 6a-b \right)/\left( +3b \right)
Class 10 | Frank | ICSE | Maths | Ratio and Proportion
If a:b=4:7, find the following(i) \left( 5a+2b \right)/\left( 5a-2b \right)(ii) \left( 6a-b \right)/\left( +3b \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,

a:b=4:7

a/b=4/7

\left( 5a+2b \right)/\left( 5a-2b \right)

Now, divide both numerator and denominator by 'b' we get,

=\left[ \left( 5a/b \right)+\left( 2b/b \right) \right]/\left[ \left( 5a/b \right)-\left( 2b/b \right) \right]

=\left[ \left( 5a/b \right)+2 \right]/\left[ \left( 5a/b \right)-2 \right]

Now, substitute the value of a and b we get,

=\left[ \left( 5\left( 4/7 \right) \right)+2 \right]/\left[ \left( 5\left( 4/7 \right) \right)-2 \right]

=\left( \left( 20/7 \right)+2 \right)/\left( \left( 20/7 \right)-2 \right)

=34/6

=17/3

Solution:

From the question it is given that,

a:b=4:7

a/b=4/7

\left( 6a-b \right)/\left( a+3b \right)

Now, divide both numerator and denominator by 'b' we get,

=\left[ \left( {6a}/{b}\; \right)-\left( {b}/{b}\; \right) \right]/\left[ \left( {a}/{b}\; \right)+\left( {3b}/{b}\; \right) \right] =\left[ \left( {6a}/{b}\; \right)-1 \right]/\left[ \left( {a}/{b}\; \right)+3 \right]

Now, substitute the value of a and b we get,

=\left[ \left( 6\left( 4/7 \right) \right)-1 \right]/\left[ \left( a/b \right)+\left( 3b/b \right) \right]

=\left( \left( 24/7 \right)-1 \right)/\left( \left( 4/7 \right)+3 \right)

=17/25

i

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