model 2 hiking & discounting Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Let the cost price of article = Rs.100

Marked price = Rs.125

SP of the article

= $(100 - 25/2)$% of 125

= $175/2$% of 125

= ${125 × 175}/{2 × 100} = 875/8$

= Rs.109$3/8$

Gain percent

= $(109{3/8} -100) = 9{3}/8$%

Using Rule 8,

Here, r = 25%, $r_1 = 12{1}/2$% = 12.5%

Profit % = ${r × (100 - r_1)}/100 - r_1$

= ${25 × (100 - {12.5})}/100 - {12.5}$

= ${25 × 87.5}/100 - 12.5$

= 21.875 - 12.5

= 9.375 = 9$3/8$%

Answer: (c)

Let the cost price be x

Mark Price

= $(1 + 20/100)x = 1.2x$

Cash price = $(1 - 30/100)1.2x$

= 0.7 × 1.2x = 0.84x

Net Loss = x - 0.84x = 0.16x

Net loss% = ${0.16x}/x × 100$ = 16%

Using Rule 8,

Here, r = 20%, $r_1$ = 30%

Profit or loss

= ${r × (100 - r_1)}/100 - r_1$

= ${20 × (100 - 30)}/100 - 30$

= 14 - 30 = –16% = 16% loss

Answer: (a)

Let the cost price be Rs.100.

Marked price = Rs.150

S.P. = ${150 × 80}/100$ = Rs.120

when S.P. = 120, C.P. = Rs.100

when S.P. = 840

C.P.= $100/120 × 840$ = Rs.700

Using Rule 8,

Here, r = 50%, $r_1$ = 20%, S.P. = Rs.840

Gain % = ${r × (100 - r_1)}/100 - r_1$

= ${50 × (100 - 20)}/100 - 20$

= ${50 × 80}/100 - 20$= 20%

We know that

Gain % = $\text"S.P. - C.P."/{C.P.} ×100$

20 = $({840 - x}/x) × 100$

20x= 84000 - 100x

120x = 84000

x = 700

∴ C.P. = Rs.700

Answer: (b)

Let cost price of article = Rs.100

Marked price of article

= ${100 × 120}/100$ = Rs.120

S.P. of article = Rs.110

Discount = 120 - 110 = Rs.10

If discount = x%, then

${120 × x}/100$ = 10

$x = {10 × 100}/120 = 25/3 = 8{1}/3$%

Using Rule 8,

Here, r = 20%, Profit = 10%

Let, discount $r_1$ = x%

Profit % = ${r × (100 - r_1)}/100 - r_1$

10 = ${20 × (100 - x)}/100 - r_1$

1000 = 2000 - 20x - 100x

–1000 = –120x

$x = 100/12 = 25/3 = 8{1}/3$%

Answer: (d)

Let Cost price = Rs.100

Marked price = Rs.120

Selling price = ${120 × 80}/100$ = Rs.96

Loss = Rs.4 and loss per cent = 4%

Using Rule 8,

Here, r = 20%, $r_1$ = 20%

Loss % = ${r × (100 - r_1)}/100 - r_1$

= ${20 × (100 - 20)}/100 - 20$

= ${20 × 80}/100 - 20$

= –4% (–ve sign shows loss)

= 4% loss