421. A fruit seller sold big, medium and small sized apples for ₹ 15, ₹ 10 and ₹ 5 respectively. The total number of apples sold were in the ratio 3 : 2 : 5. Find the average cost of an apple.

1. 1. ₹ 8

   
   
   

   2. ₹ 10

   
   
   

   3. ₹ 9

   
   
   

   4. ₹ 7

   
   
   

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   Ratio of values
   = 15 × 3 : 10 × 2 : 5 × 5
   = 45 : 20 : 25
   

   ∴   Required average cost =	45 + 20 + 25
   	10

   
   

   =	90	= ₹ 9
   	10

   Correct Option: C

   Ratio of values
   = 15 × 3 : 10 × 2 : 5 × 5
   = 45 : 20 : 25
   

   ∴   Required average cost =	45 + 20 + 25
   	10

   
   

   =	90	= ₹ 9
   	10

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422. In a school, the ratio of boys to girls is 4 : 3 and the ratio of girls to teachers is 8 : 1. The ratio of students to teachers is :

1. 1. 56 : 3

   
   
   

   2. 55 : 1

   
   
   

   3. 49 : 3

   
   
   

   4. 56 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Boys : Girls
   = 4 : 3 = 32 : 24
   Girls : Teachers
   = 8 : 1 = 24 : 3
   ∴  Boys : Girls : Teachers
   = 32 : 24 : 3
   ∴  Required ratio
   = (32 + 24) : 3 = 56 : 3

   Correct Option: A

   Boys : Girls
   = 4 : 3 = 32 : 24
   Girls : Teachers
   = 8 : 1 = 24 : 3
   ∴  Boys : Girls : Teachers
   = 32 : 24 : 3
   ∴  Required ratio
   = (32 + 24) : 3 = 56 : 3

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423. If	3x + 5	=	2	, then the value of x is
     	5x − 2		3

1. 1. 11

   
   
   

   2. 19

   
   
   

   3. 23

   
   
   

   4. 7

   
   
   

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1. View Hint View Answer Discuss in Forum

   3x + 5	=	2
   5x − 2		3

   
   ⇒  10x – 4 = 9x + 15
   ⇒  10x – 9x = 15 + 4 = 19
   ⇒  x = 19

   Correct Option: B

   3x + 5	=	2
   5x − 2		3

   
   ⇒  10x – 4 = 9x + 15
   ⇒  10x – 9x = 15 + 4 = 19
   ⇒  x = 19

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424. A, B and C are batsmen. The ratio of the runs scored by them in a certain match are given below : A : B = 5 : 3 and B : C = 4 : 5. In all they scored 564 runs. The number of runs scored by B is:

1. 1. 124

   
   
   

   2. 104

   
   
   

   3. 114

   
   
   

   4. 144

   
   
   

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1. View Hint View Answer Discuss in Forum

   A : B = 5 : 3
   B : C = 4 : 5
   ∴  A : B : C
   = 5 × 4 : 3 × 4 : 3 × 5
   = 20 : 12 : 15
   Sum of ratios
   = 20 + 12 + 15 = 47
   ∴  Runs scored by B
   

   =	12	× 564 = 144
   	47

   Correct Option: D

   A : B = 5 : 3
   B : C = 4 : 5
   ∴  A : B : C
   = 5 × 4 : 3 × 4 : 3 × 5
   = 20 : 12 : 15
   Sum of ratios
   = 20 + 12 + 15 = 47
   ∴  Runs scored by B
   

   =	12	× 564 = 144
   	47

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425. If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and (a + b + c) = 14, then the value of c is

1. 1. 6

   
   
   

   2. 7

   
   
   

   3. 8

   
   
   

   4. 14

   
   
   

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1. View Hint View Answer Discuss in Forum

   a + b	=	b + c	=	c + a	= k
   6		7		8

   
   ⇒  a + b = 6k; b + c = 7k;
   c + a = 8k
   ∴  a + b + b + c + c + a
   = 6k + 7k + 8k
   ⇒  2 (a + b + c) = 21k
   

   ⇒  2 × 14 = 21k ⇒ k =	4
   	3

   
   ∴  c = (a + b + c) – (a + b)
   

   = 14 − 6 ×	4	= 14 − 8 = 6
   	3

   Correct Option: A

   a + b	=	b + c	=	c + a	= k
   6		7		8

   
   ⇒  a + b = 6k; b + c = 7k;
   c + a = 8k
   ∴  a + b + b + c + c + a
   = 6k + 7k + 8k
   ⇒  2 (a + b + c) = 21k
   

   ⇒  2 × 14 = 21k ⇒ k =	4
   	3

   
   ∴  c = (a + b + c) – (a + b)
   

   = 14 − 6 ×	4	= 14 − 8 = 6
   	3

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