136. What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2 ?

1. 1. 5 is subtracted

   
   
   

   2. 10 is added

   
   
   

   3. 7 is added

   
   
   

   4. 10 is subtracted

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the number x be added.
   

   ∴	17 + x	=	1
   	24 + x		2

   
   ⇒  34 + 2x = 24 + x
   ⇒  2x – x = 24 – 34
   ⇒  x = –10
   Hence, 10 should be subtracted.

   Correct Option: D

   Let the number x be added.
   

   ∴	17 + x	=	1
   	24 + x		2

   
   ⇒  34 + 2x = 24 + x
   ⇒  2x – x = 24 – 34
   ⇒  x = –10
   Hence, 10 should be subtracted.

---

137. Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is

1. 1. 36

   
   
   

   2. 48

   
   
   

   3. 56

   
   
   

   4. 64

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the numbers be 4x and 7x.
   

   ∴	4x + 4	=	3
   	7x + 4		5

   
   ⇒  21x + 12 = 20x + 20
   ⇒  21x – 20x = 20 – 12
   ⇒  x = 8
   ∴  Larger number
   = 7x = 7 × 8 = 56
   Second Method :
   a = 4, b = 7, c = 3, d = 5, x = 4
   

   Larger number =	xa(c − d)
   	ad − bc

   
   

   =	4 × 7(3 − 5)
   	4 × 5 − 3 × 7

   
   

   =	4 × 7 × (−2)	= 56
   	20 − 21

   Correct Option: C

   Let the numbers be 4x and 7x.
   

   ∴	4x + 4	=	3
   	7x + 4		5

   
   ⇒  21x + 12 = 20x + 20
   ⇒  21x – 20x = 20 – 12
   ⇒  x = 8
   ∴  Larger number
   = 7x = 7 × 8 = 56
   Second Method :
   a = 4, b = 7, c = 3, d = 5, x = 4
   

   Larger number =	xa(c − d)
   	ad − bc

   
   

   =	4 × 7(3 − 5)
   	4 × 5 − 3 × 7

   
   

   =	4 × 7 × (−2)	= 56
   	20 − 21

---

---

138. The students in three classes are in the ratio 4 : 6 : 9. If 12 students are increased in each class, the ratio changes to 7 : 9 : 12. Then the total number of students in the three classes before the increase is

1. 1. 95

   
   
   

   2. 76

   
   
   

   3. 100

   
   
   

   4. 114

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the original number of students be 4x , 6x and 9x.
   

   ∴	4x + 12	=	7
   	6x + 12		9

   
   ⇒  42x + 84 = 36x + 108
   ⇒  42x – 36x = 108 – 84
   ⇒  6x = 24
   ⇒  x = 4
   ∴  Required number of students
   = 19x = 19 × 4 = 76

   Correct Option: B

   Let the original number of students be 4x , 6x and 9x.
   

   ∴	4x + 12	=	7
   	6x + 12		9

   
   ⇒  42x + 84 = 36x + 108
   ⇒  42x – 36x = 108 – 84
   ⇒  6x = 24
   ⇒  x = 4
   ∴  Required number of students
   = 19x = 19 × 4 = 76

---

139. The total number of students in a school was 660. The ratio between boys and girls was 13 : 9. After some days, 30 girls joined the school and some boys left the school and new ratio between boys and girls became 6 : 5. The number of boys who left the school is :

1. 1. 50

   
   
   

   2. 40

   
   
   

   3. 30

   
   
   

   4. 60

   
   
   

---

1. View Hint View Answer Discuss in Forum

   In the first case,
   

   Boys = 660 ×	13	= 390
   	22

   
   

   Girls = 660 ×	9	= 270
   	22

   
   If x boys leave the school, then
   

   390 − x	=	6
   270 + 30		5

   
   ⇒  390 – x = 360
   ⇒  x = 390 – 360 = 30

   Correct Option: C

   In the first case,
   

   Boys = 660 ×	13	= 390
   	22

   
   

   Girls = 660 ×	9	= 270
   	22

   
   If x boys leave the school, then
   

   390 − x	=	6
   270 + 30		5

   
   ⇒  390 – x = 360
   ⇒  x = 390 – 360 = 30

---

---

140. If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wage in the ratio 22 : 25, then the ratio by which the total wage of the workers should be decreased is

1. 1. 6 : 5

   
   
   

   2. 5 : 6

   
   
   

   3. 3 : 7

   
   
   

   4. 3 :5

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Required ratio
   = 15 × 22 : 11 × 25 = 6 : 5

   Correct Option: A

   Required ratio
   = 15 × 22 : 11 × 25 = 6 : 5

---