Question

Find the single discount which is equilent to two successive discounts of 20% and 5%.

Answer 1

Mp = 100

1st discount = 20% of 100 = 20

since, 100 - 20 = 80

2nd discount = 5% if 80 = 4

sp= 80-4 = 76

Single Equivalent Discount  = MP - SP

= 100 -76 = 24

Since,The discount of 24 is on 100

Required single discount  = 24%

Answer 2

$\mathfrak{Answer:}$

= 24%.

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

$\underline{\bold{Given\:in\:the\:Question:}}$

• First discount = d₁ = 20%.
• Second discount = d₂ = 5%.

$\huge{\underline{\underline{\textbf{Method No. 1.}}}}$

Let the equivalent discount be D%.

We know that ,

$\boxed{\bold{1-\dfrac{D}{100}=\left(1-\dfrac{d_1}{100}\right)\left(1-\dfrac{d_2}{100}\right)}}\\\\\\\implies\tt{1-\dfrac{D}{100}=\left(1-\dfrac{20}{100}\right)\left(1-\dfrac{5}{100}\right)}\\\\\\\implies\tt{\dfrac{100-D}{100}=\dfrac{100-20}{100}\times\dfrac{100-5}{100}}\\\\\\\implies\tt{\dfrac{100-D}{100}=\dfrac{80}{100}\times\dfrac{95}{100}}\\\\\\\implies\tt{100-D=76}\\\\\\\implies\tt{D=100-76}\\\\\\\therefore\tt{\quad D=24\%.}$

$\huge{\underline{\underline{\textbf{Method No.2}}}}$

$\tt{Let\:\:A=20\%\quad\&\quad B=5\%.}\\\\\\\boxed{\bold{Single\:discount=(A+B)-\dfrac{AB}{100}}}\\\\\\\tt{=(20+5)-\dfrac{20\times 5}{100}}\\\\\\\tt{=25-1}\\\\\\\tt{=24\%.}\\\\\\\\\boxed{\boxed{\bold{Single\:discount=24\%.}}}$