6. If a : b = c : d = e : f = 1 : 2, then (pa + qc + re) : (pb + qd + rf) is equal to :

1. 1. p : (q + r)

   
   
   

   2. (p + q) : r

   
   
   

   3. 2 : 3

   
   
   

   4. 1 : 2

   
   
   

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   a	=	c	=	e	=	1
   b		d		f		2

   
   

   ⇒	pa	=	qc	=	re	=	1
   	pb		qd		rf		2

   
   

   ⇒	pa + qc + re	=	1	or   1 : 2
   	pb + qd + rf		2

   Correct Option: D

   a	=	c	=	e	=	1
   b		d		f		2

   
   

   ⇒	pa	=	qc	=	re	=	1
   	pb		qd		rf		2

   
   

   ⇒	pa + qc + re	=	1	or   1 : 2
   	pb + qd + rf		2

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7. If p : q = r : s = t : u = 2 : 3, then (mp + nr + ot) : (mq + ns +ou) is equal to :

1. 1. 1 : 3

   
   
   

   2. 1 : 2

   
   
   

   3. 2 : 3

   
   
   

   4. 3 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   If	a	=	c	=	e	, then each of
   	b		d		f

   
   

   these ratios is equal to	a + c + e
   	b + d + f

   
   Here,
   

   p	=	r	=	t	=	2
   q		s		u		3

   
   

   ⇒	mp	=	nr	=	ot	=	2
   	mq		ns		ou		3

   
   

   ⇒	mp + nr + ot	:	2	or   2 : 3
   	mq + ns + ou		3

   Correct Option: C

   If	a	=	c	=	e	, then each of
   	b		d		f

   
   

   these ratios is equal to	a + c + e
   	b + d + f

   
   Here,
   

   p	=	r	=	t	=	2
   q		s		u		3

   
   

   ⇒	mp	=	nr	=	ot	=	2
   	mq		ns		ou		3

   
   

   ⇒	mp + nr + ot	:	2	or   2 : 3
   	mq + ns + ou		3

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8. If   x =	1	y and y =	1	z
   	3		2

   then x : y : z, is equal to :

1. 1. 3 : 2 : 1

   
   
   

   2. 1 : 2 : 6

   
   
   

   3. 1 : 3 : 6

   
   
   

   4. 2 : 4 : 6

   
   
   

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   x =	1	y ⇒ x : y = 1 : 3
   	3

   Again, y =	1	z ⇒ y : z
   	2

   
   = 1 : 2 = 3 : 6
   ∴  x : y : z = 1 : 3 : 6

   Correct Option: C

   x =	1	y ⇒ x : y = 1 : 3
   	3

   Again, y =	1	z ⇒ y : z
   	2

   
   = 1 : 2 = 3 : 6
   ∴  x : y : z = 1 : 3 : 6

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9. If a : b = 7 : 9 and b : c =15 : 7, then what is a : c?

1. 1. 5 : 3

   
   
   

   2. 3 : 5

   
   
   

   3. 7 : 21

   
   
   

   4. 7 : 15

   
   
   

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1. View Hint View Answer Discuss in Forum

   a : c = (a : b) × (b : c)
   

   =	7	×	15	=	15	= 5 : 3
   	9		7		9

   
   Second Method :
   A : C = 7 × 15 : 9 × 7 = 5 : 3

   Correct Option: A

   a : c = (a : b) × (b : c)
   

   =	7	×	15	=	15	= 5 : 3
   	9		7		9

   
   Second Method :
   A : C = 7 × 15 : 9 × 7 = 5 : 3

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10. The ratio of incomes of A and B is 5 : 6. If A gets ₹ 1,100 less than B, their total income (in rupees) is

1. 1. 9,900

   
   
   

   2. 12,100

   
   
   

   3. 14,400

   
   
   

   4. 10,000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the income of A be ₹ 5x and that of B be ₹ 6x.
   According to the question,
   6x –5x =1100
   ∴  Total income = 5x + 6x = ₹ 11x
   = ₹ (11×1100) = ₹ 12100

   Correct Option: B

   Let the income of A be ₹ 5x and that of B be ₹ 6x.
   According to the question,
   6x –5x =1100
   ∴  Total income = 5x + 6x = ₹ 11x
   = ₹ (11×1100) = ₹ 12100

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