Question

The advertised price of a tv is x, what will be its selling price after deduction of two successive discount at the rates of y% and z% ?


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Answer 1

Step-by-step explanation:

For example, we have an article costing Rs 10000 which is its' Marked Price or Tagged Price. When we give discounts of 10% and 20%, successively on this article; the selling price we get after this, is said to be the Selling Price after Successive Discounts.

To be more clear, we will have two Marked Price (for understanding) in successive discounts.

Solving the above example, we would get:

Solution:

Given,

Marked Price of an article (M.P.)= Rs 10000

Successive Discounts = 10% and 20%

Now,

S.P. = MP - 10% of MP

= 10000 - 10% x 10000

= 10000 - 1000

= Rs 9000

Again, 

Required S.P. = Rs 9000 - 20% of RS 9000

= 9000 - 20% x 9000

= 9000 - 1800

= Rs 7200

So, this is how we solve these types of questions having successive discounts.

Generating Formulae:

But, can we get some Formulae to do the work a lot easier and faster? Instead of solving the question in two steps, can we just find the solution within one step? Okay, Let's find it out by generating the formulae.

First of all, we need to understand this:

      S.P. = M.P. - d% of M.P.

or, S.P. = M.P. (1 - d%)

or, S.P. = M.P. (1 -d/100) .... (i)

Above, we took Marked Price common in the exdivssion to bring the factors of the formulae.

Successive Discounts can be of two types: Same discount rates or different discount rates.

Let, M.P. = x

Discount 1 = y%

Discount 2 = z%

Formula for Same Discount Rates:

We have, 

S.P. = x (1- y%)

or, S.P. = x(1 - y/100) .... (a)

If we have same discount rates, Discount 2 = y%

Now, our M.P. is exdivssion generated in equation (a)

This means:

M.P. = x(1 -y/100)

Discount = y% of M.P.

Now,

S.P. = M.P. - d% of M.P.

= x (1- y/100) - {y% of x(1-y/100)}

= x (1- y/100) - {y/100 * x(1-y/100)}

= x (1- y/100) (1 - y/100)

= x (1- y/100)^2

So, when there is successive discount of same rates then, we have the following formula:

S.P. = M.P. (1 - Discount /100)^2

Answer 2

Marked Price of an article (M.P.)= Rs

10000

1 @ 50

Successive Discounts = 10% and 20%

Now,

S.P. = MP - 10% of MP

= 10000 - 10% x 10000

= Rs 9000

Again,

Required S.P. = Rs 9000 - 20% of RS 9000

= 9000 - 20% x 9000

= 9000 - 1800

1 @ 50

= Rs 7200

So, this is how we solve these types of questions having successive discounts.

Generating Formulae:

But, can we get some Formulae to do the work a lot easier and faster? Instead of solving the question in two steps, can we just find the solution within one step? Okay, Let's find it out by generating the formulae.

First of all, we need to understand this:

S.P. = M.P. - d% of M.P.

or, S.P. = M.P. (1-d%)

or, S.P. = M.P. (1-d/100) .... (i)

Above, we took Marked Price common in

the exdivssion to bring the factors of the formulae.

Successive Discounts can be of two types: Same discount rates or different discount rates.

Let, M.P. = x

Discount 1 = y%

Discount 2 =z%

Formula for Same Discount Rates:

We have,

We have,

S.P. = x (1- y%)

or, S.P. = x(1-y/100) .... (a)

If we have same discount rates, Discount 2 = y%

Now, our M.P. is exdivssion generated in equation (a)

This means:

M.P. = = x(1-y/100)

Discount = y% of M.P

M.P. = x(1-y/100)

Discount = y% of M.P.

Now,

S.P. = M.P. - d% of M.P.

= x (1-y/100) - {y% of x(1-y/100)}

= x (1-y/100) - {y/100 * x(1-y/100)}

= x (1-y/100) (1 - y/100)

= x (1-y/100)^2

= x (1-y/100) - {y% of x(1-y/100)}

= x (1-y/100) - {y/100 * x(1-y/100)}

= x (1-y/100) (1 - y/100)

= x (1-y/100)^2

So, when there is successive discount of same rates then, we have the following formula:

S.P. = M.P. (1 - Discount /100)^2