451. A man engaged a servant on the condition that he would pay him ₹ 90 and a turban after service of one year. He served only for nine months and received the turban and an amount of ₹ 65. The price of turban is

1. 1. ₹ 25

   
   
   

   2. ₹ 18.75

   
   
   

   3. ₹ 10

   
   
   

   4. ₹ 2.50

   
   
   

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1. View Hint View Answer Discuss in Forum

   12 months’ salary = ₹ 90 + turban
   ∴  9 months’ salary
   

   = (₹ 90 + turban) ×	9
   	12

   
   

   = ₹ 90 ×	3	+	3	turban
   	4		4

   
   

   = ₹	135	+	3	turban
   	2		4

   
   

   ∴  ₹	135	+	3	turban
   	2		4

   
   = ₹ 65 + turban
   

   ∴	1	turban =	135	− 65 = ₹	5
   	4		2		2

   
   

   ∴  Turban ⇒	5	× 4 = ₹ 10
   	2

   Correct Option: C

   12 months’ salary = ₹ 90 + turban
   ∴  9 months’ salary
   

   = (₹ 90 + turban) ×	9
   	12

   
   

   = ₹ 90 ×	3	+	3	turban
   	4		4

   
   

   = ₹	135	+	3	turban
   	2		4

   
   

   ∴  ₹	135	+	3	turban
   	2		4

   
   = ₹ 65 + turban
   

   ∴	1	turban =	135	− 65 = ₹	5
   	4		2		2

   
   

   ∴  Turban ⇒	5	× 4 = ₹ 10
   	2

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452. If the operation ‘ * ’ is defined by a * b = a + b – ab, then 5 * 7 equals

1. 1. 12

   
   
   

   2. –47

   
   
   

   3. –23

   
   
   

   4. 35

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∵  a * b = a + b – ab
   ∴  5 * 7 = 5 + 7 – 5 × 7 = 12 – 35
   = – 23

   Correct Option: C

   ∵  a * b = a + b – ab
   ∴  5 * 7 = 5 + 7 – 5 × 7 = 12 – 35
   = – 23

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453. A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number ?

1. 1. 6

   
   
   

   2. 3.5

   
   
   

   3. 8

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Suppose number is x.
   ∴  3 (2x + 9) = 75
   ⇒  6x + 27 = 75
   ⇒  6x = 48 ⇒ x = 8

   Correct Option: C

   Suppose number is x.
   ∴  3 (2x + 9) = 75
   ⇒  6x + 27 = 75
   ⇒  6x = 48 ⇒ x = 8

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454. The sum of two number is 8 and their product is 15. The sum of their reciprocals is

1. 1. 8

      15

   
   
   

   2. 15

      8

   
   
   

   3. 23

   
   
   

   4. 7

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the numbers be x and y,
   then
   x + y = 8 ....... (i)
   xy = 15 ...... (ii)
   Dividing equation (i) by (ii)
   

   x + y	=	8	⇒	x	+	y	=	8
   xy		15		xy		xy		15

   
   

   1	+	1	=	8
   y		x		15

   Correct Option: A

   If the numbers be x and y,
   then
   x + y = 8 ....... (i)
   xy = 15 ...... (ii)
   Dividing equation (i) by (ii)
   

   x + y	=	8	⇒	x	+	y	=	8
   xy		15		xy		xy		15

   
   

   1	+	1	=	8
   y		x		15

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455. In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 36, then the dividend is

1. 1. 2706

   
   
   

   2. 2796

   
   
   

   3. 2736

   
   
   

   4. 2826

   
   
   

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1. View Hint View Answer Discuss in Forum

   Divisor = 5 × remainder
   = 5 × 36 = 180
   Again, Divisor = 12 × quotient
   ∴  180 = 12 × quotient
   

   ∴  Quotient =	180	= 15
   	12

   
   ∴  Dividend = Divisor × Quotient + Remainder
   = 180 × 15 + 36
   = 2700 + 36 = 2736

   Correct Option: C

   Divisor = 5 × remainder
   = 5 × 36 = 180
   Again, Divisor = 12 × quotient
   ∴  180 = 12 × quotient
   

   ∴  Quotient =	180	= 15
   	12

   
   ∴  Dividend = Divisor × Quotient + Remainder
   = 180 × 15 + 36
   = 2700 + 36 = 2736

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