THEOREMS ON PROPORTIONS - PUNJAB-BOARD / 10TH-CLASS / MATHEMATICS / 1-10-MATHS-FULL-10TH-CLASS-NBF-2024 / VARIATIONS / THEOREMS-ON-PROPORTIONS

If four quantities $a, b, c$ and $d$ form a proportion, then many other useful properties may be deduced by the properties of fractions.

If $a:b = c:d$ , then $b:a = d:c$

If $3m:2n = p:2q$ , then $2n:3m = 2q:p$

Solution: Since $3m:2n = p:2q$

$∴ \frac{3 m}{2 n} = \frac{p}{2 q}$

By invertedo theorem

$\frac{2 n}{3 m} = \frac{2 q}{p}$

i.e., $2n:3m = 2q:p$

If $a:b = c:d$ , then $a:c = b:d$

If $3p + 1:2q = 5r:7s$ , then prove that $3p + 1:5r = 2q:7s$

Solution: Given that $3p + 1:2q = 5r:7s$

$\frac{3 p + 1}{2 q} = \frac{5 r}{7 s}$

By alternando theorem

$\frac{3 p + 1}{5 r} = \frac{2 q}{7 s}$

Thus, $3p + 1:5r = 2q:7s$