Answer: Option C. -> Rs.1,368
Answer: (c)Using Rule 5,Single equivalent discount for two successive discounts of 20% and 10%= $(20 + 10 - {20 × 10}/100)%$ = 28%Now , single discount for 28% and 5%= $(28 + 5 - {28 × 5}/100)%$= (33 - 1.4) % = 31.6%Required selling price of bicycle at cash payment= (100 - 31.6) % of Rs.2000= ${2000 × 68.4}/100$ = Rs.1368

Answer: Option B. -> 5%
Answer: (b)Equivalent discount= $10 + 5 - {10 × 5}/100 = 14.5%$CP (for buyer)= 85.5% of Rs.200000= Rs.$({85.5 × 200000}/100)$ = Rs.171000SP = Rs.179550Gain = Rs.(179550 –171000) = Rs.8550Gain % = $8550/171000 × 100 =5%$Using Rule 3,Here, M.P. = 200000,S.P. is C.P. byer for $D_1 = 5%, D_2$ = 10%S.P.= M.P.$({100 - D_1}/100)({100 - D_2}/100)$= 200000$({100 - 5}/100)({100 - 10}/100)$= 20 × 95 × 90C.P. for buyer =171000S.P. = 179550Profit =S.P. - $\text"C.P."/\text"C.P" ×100%$= $8550/171000$ × 100 = 5%

Answer: Option A. -> Rs.7.20
Answer: (a)Using Rule 5,Single equivalent discount of two successive discounts of 36% and 4%= 36 + 4 - ${36 × 4}/100$= 40 - 1.44 = 38.56Percentage difference= 40 - 38.56 = 1.44Required difference= 500 × ${1.44}/100$ = Rs.7.20

Answer: Option C. -> Rs.15
Answer: (c)Using Rule 5,Single equivalent discount of two consecutive discount of 30% and 10%= 30 + 10 - ${30 × 10}/100 = 37%$Required difference= 40% of 500 - 37% of 500= 3% of 500= $500 × 3/100$ = Rs.15

Answer: Option B. -> Rs.25
Answer: (b)Using Rule 5,Case I,Discount = ${30 × 2000}/100$ = Rs.600Single equivalent discount for discounts of 25% and 5%.= $(25 + 5 - {25 × 5}/100)$%= (30 - 1.25)% = 28.75%Discount = ${28.75 × 2000}/100$ = Rs.575Difference = Rs.(600 - 575) = Rs.25

Answer: Option D. -> 9$3/8$%
Answer: (d)Let the cost price of article = Rs.100Marked price = Rs.125SP 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: Option C. -> 16%
Answer: (c)Let the cost price be xMark Price= $(1 + 20/100)x = 1.2x$Cash price = $(1 - 30/100)1.2x$= 0.7 × 1.2x = 0.84xNet Loss = x - 0.84x = 0.16xNet 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: Option B. -> 8$1/3$%
Answer: (b)Let cost price of article = Rs.100Marked price of article= ${100 × 120}/100$ = Rs.120S.P. of article = Rs.110Discount = 120 - 110 = Rs.10If 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: Option A. -> Rs.700
Answer: (a)Let the cost price be Rs.100.Marked price = Rs.150S.P. = ${150 × 80}/100$ = Rs.120when S.P. = 120, C.P. = Rs.100when S.P. = 840C.P.= $100/120 × 840$ = Rs.700Using Rule 8,Here, r = 50%, $r_1$ = 20%, S.P. = Rs.840Gain % = ${r × (100 - r_1)}/100 - r_1$= ${50 × (100 - 20)}/100 - 20$= ${50 × 80}/100 - 20$= 20%We know thatGain % = $\text"S.P. - C.P."/{C.P.} ×100$20 = $({840 - x}/x) × 100$20x= 84000 - 100x120x = 84000x = 700∴ C.P. = Rs.700

Answer: Option D. -> 4% loss
Answer: (d)Let Cost price = Rs.100Marked price = Rs.120Selling price = ${120 × 80}/100$ = Rs.96Loss = 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