166. A shopkeeper lists the price of an article as ₹ 500. But he gives a certain discount which allows the buyer to pay ₹ 500 for the article including 10% sales tax. The rate of discount is

1. 1. 10%

   
   
   

   2. 10	1	%
      	11

   
   
   

   3. 9	1	%
      	11

   
   
   

   4. 11%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the S.P. be x (without tax).
   

   ∴  x + x ×	10	= 500
   	100

   
   

   ⇒	11x	= 500 ⇒ x = ₹	5000
   	10		11

   
   

   ∴  Discount = 500 −	5000
   	11

   
   

   =	500
   	11

   
   

   Discount per cent =	500	× 100
   	11 × 500

   
   

   =	100	% or 9	1	%
   	11		11

   Correct Option: C

   Let the S.P. be x (without tax).
   

   ∴  x + x ×	10	= 500
   	100

   
   

   ⇒	11x	= 500 ⇒ x = ₹	5000
   	10		11

   
   

   ∴  Discount = 500 −	5000
   	11

   
   

   =	500
   	11

   
   

   Discount per cent =	500	× 100
   	11 × 500

   
   

   =	100	% or 9	1	%
   	11		11

---

167. With a 5 % discount on the cost of sugar, a buyer could purchase 2 kg more sugar for ₹ 608. Selling price of sugar is :

1. 1. ₹ 15.50

   
   
   

   2. ₹ 15

   
   
   

   3. ₹ 16.50

   
   
   

   4. ₹ 16

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the original S.P. of sugar be x per kg.
   

   S.P. after discount = ₹	95x	per kg
   	100

   
   

   = ₹	19x	per kg
   	20

   
   

   ∴	608	−	608	= 2
   	19x/20		x

   
   

   ⇒  608		20	−	1		= 2
   		19x		x

   
   

   ⇒	608	= 2 ⇒ x =	608	= ₹ 16
   	19x		19 × 2

   Let the original S.P. of sugar be x per kg.
   

   S.P. after discount = ₹	95x	per kg
   	100

   
   

   = ₹	19x	per kg
   	20

   
   

   ∴	608	−	608	= 2
   	19x/20		x

   
   

   ⇒  608		20	−	1		= 2
   		19x		x

   
   

   ⇒	608	= 2 ⇒ x =	608	= ₹ 16
   	19x		19 × 2

   Correct Option: D

   Let the original S.P. of sugar be x per kg.
   

   S.P. after discount = ₹	95x	per kg
   	100

   
   

   = ₹	19x	per kg
   	20

   
   

   ∴	608	−	608	= 2
   	19x/20		x

   
   

   ⇒  608		20	−	1		= 2
   		19x		x

   
   

   ⇒	608	= 2 ⇒ x =	608	= ₹ 16
   	19x		19 × 2

---

---

168. During a month-long annual sale, a shopkeeper sells his goods at a discount of 50%. But in the last week, he offers an additional discount of 40%. If the original price of a shirt is ₹ x, then the price, (in rupees) during the last week of the sale will be

1. 1. 90% of x

   
   
   

   2. 70% of x

   
   
   

   3. 30% of x

   
   
   

   4. 10% of x

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Single equivalent discount =		50 + 40 −	50 × 40		% = 70%
   			100

   
   ∴  Required price of shirt = 30% of x

   Correct Option: C

   Single equivalent discount =		50 + 40 −	50 × 40		% = 70%
   			100

   
   ∴  Required price of shirt = 30% of x

---

169. Ramesh bought 10 cycles for ₹ 500 each. He spent ₹ 2,000 on the repair of all cycles. He sold five of them for ₹ 750 each and the remaining for ₹ 550 each. Then the total gain or loss % is

1. 1. Gain of 8	1	%
      	3

   
   
   

   2. Loss of 8	1	%
      	3

   
   
   

   3. Gain of 7	2	%
      	3

   
   
   

   4. Loss of 7	1	%
      	7

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Total actual C.P.
   = ₹ (500 × 10 + 2000) = ₹ 7000
   Total S.P.
   = ₹ (5 × 750 + 5× 550)
   = ₹ (3750 + 2750) = ₹ 6500
   Loss = 7000 – 6500 = ₹ 500
   

   Loss percent =	500	× 100 =	50	= 7	1	%
   	7000		7		7

   Correct Option: D

   Total actual C.P.
   = ₹ (500 × 10 + 2000) = ₹ 7000
   Total S.P.
   = ₹ (5 × 750 + 5× 550)
   = ₹ (3750 + 2750) = ₹ 6500
   Loss = 7000 – 6500 = ₹ 500
   

   Loss percent =	500	× 100 =	50	= 7	1	%
   	7000		7		7

---

---

170. A fan is listed at ₹ 1,400 and the discount offered is 10%. What additional discount must be given to bring the net selling price to ₹ 1,200 ?

1. 1. 16	2	%
      	3

   
   
   

   2. 5%

   
   
   

   3. 4	16	%
      	21

   
   
   

   4. 6%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Marked price of the fan = ₹ 1400
   SP after allowing a discount of 10% = 90% of 1400
   

   =	1400 × 90	= ₹ 1260
   	100

   
   Second discount = ₹ (1260 – 1200 ) = ₹ 60
   Let the second discount be x%.
   ∴  x% of 1260 = 60
   

   ⇒ x =	60 × 100	=	100	= 4	16	%
   	1260		21		21

   Correct Option: C

   Marked price of the fan = ₹ 1400
   SP after allowing a discount of 10% = 90% of 1400
   

   =	1400 × 90	= ₹ 1260
   	100

   
   Second discount = ₹ (1260 – 1200 ) = ₹ 60
   Let the second discount be x%.
   ∴  x% of 1260 = 60
   

   ⇒ x =	60 × 100	=	100	= 4	16	%
   	1260		21		21

---