model 3 successive discount Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Let the second discount be x per cent.

According to the question,

$450 × {100 - 10}/100 × {100 - x}/100$ = 344.25

100 - x = ${344.25 × 100 × 100}/{450 × 90}$

100 - x = 85

x = 100 - 85 = 15%.

Using Rule 3,

Here, M.P. = Rs.450, S.P. = Rs.344.25, $D_1 = 10%, D_2$ = ?

S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$

$344.25 = 450 × ({100 - 10}/100)({100 - D_2}/100)$

$3442500/{450 × 90} = (100 - D_2)$

$85 = 100 - D_2 ⇒ D_2$ = 15%

Answer: (b)

Let 'x' be the marked price Single Discount = 15%

100 - 15 = 85

85% of x = 17,000

$x = {17,000}/85 × 100$ = Rs.20,000

Required SP

= $20,000 × 95/100 × 90/100$

= 180 × 95 = Rs.17100

M.P. = ${S.P. × 100}/{100 - D}$

= ${17000 × 100}/{100 - 15}$

= ${17000 × 100}/85$

M.P. = 20000

Also,

S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$

= 20000$({100 - 5}/100)({100 - 10}/100)$

= $20000 × 95/100 × 90/100$

= 180 × 95 = Rs.17100

Answer: (d)

Using Rule 5,

Let the original price be Rs.100

Increased price = Rs.130

Equivalent discount

= $(10 + 10 - {10 × 10}/100)$ = 19%

Ultimate price of the article = 81% of 130 = 105.3

i.e. increase by 5.3%.

Answer: (d)

Using Rule 5,

Equivalent discount for two successive discounts of 8% and 8%

= $(8 + 8 - {8 × 8}/100)$%

= (16–0.64) % = 15.36 %

SP = (100 –15.36) % of 900

= Rs.$({84.64 × 900}/100)$ = Rs.761.76

For a single discount of 16%,

SP = 84% of 900

= Rs.$({84 × 900}/100)$ = Rs.756

Certainly seller will lose in this case.

Loss = Rs. (761.76 - 756) = Rs.5.76

Answer: (b)

Total discount

=Rs.(820 - 570.72) = Rs.249.28

First discount = $820 × 20/100$ = Rs.164

Second discount

= Rs.(249.28 - 164) = Rs.85.28

Price of the article after first discount

= Rs.(820 - 164) = Rs.656

If the second discount be x% , then

x% of 656 = 85.28

$x = {85.28 × 100}/656 = 13%$

Using Rule 3,

Here, M.P. = Rs.820, S.P. = 570.72, $D_1 = 20%, D_2$ = ?

S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$

$570.72 = 820 ({100 - 20}/100)({100 - D_2}/100)$

$5707200/{820 × 80} = 100 - D_2$

$100 - D_2 = 87 ⇒ D_2$ = 13%

Answer: (a)

Using Rule 5,

Effective discount

= 25 + 15 - ${25 × 15}/100$

= 40 - 3.75 = 36.25 %

CP for buyer

= (100 - 36.25) % of 800

= ${63.75 × 800}/100$ = Rs.510

To gain 20%,

SP = Rs.$({120 × 510}/100)$ = Rs.612

Let the list price be Rs.x.

90% of x = Rs.612

${90x}/100$ = 612

$x = 61200/90$ = Rs.680