Question

find the single discount which is equivalent to successive discount of 20% and 50%​

Answer 1

successive discount =x+y+xy/100
= 20+50 +20×50/100
70+ 1000/100
70+10
=80
80% is answer

Answer 2

$\mathfrak{Step-By-Step\:Explanation:}$

$\underline{\mathfrak{Method\:\:no.1}}\\\\\\\tt{Let\:A=20\%\:and\:B=50\%.}\\\\\\\boxed{\bold{Equivalent\:Discount=(A+B)-\dfrac{AB}{100}}}\\\\\\\tt{=\left((20+50)-\dfrac{(20\times 50)}{100}\right)\%}\\\\\\\tt{=\left(70-\dfrac{1000}{100}\right)}\\\\\\\tt{=70-10}\\\\\\=60\%.\\\\\\\\\underline{\mathfrak{Method\:\:no.2}}\\\\\\\boxed{\bold{1-\dfrac{D}{100}=\left(1-\dfrac{d_1}{100}\right)\left(1-\dfrac{d_2}{100}\right)...}}$

$\implies\bold{1-\dfrac{D}{100}=\left(1-\dfrac{20}{100}\right)\left(1-\dfrac{50}{100}\right)}\\\\\\\implies\bold{\dfrac{100-D}{100}=\dfrac{100-20}{100}\times\dfrac{100-50}{100}}\\\\\\\implies\bold{\dfrac{100-D}{100}=\dfrac{80\times 50}{10000}}\\\\\\\implies\bold{100-D=40}\\\\\\\implies\bold{D=100-40}\\\\\\\implies\bold{D=60\%.}\\\\\\\\\boxed{\boxed{\bold{Equivalent\;Discount=60\%.}}}$