396. The ratio of number of boys and girls in a school of 720 students is 7 : 5. How many more girls should be admitted to make the ratio 1 : 1 ?

1. 1. 90

   
   
   

   2. 120

   
   
   

   3. 220

   
   
   

   4. 240

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Boys : Girls = 7 : 5
   

   Number of boys =	7	× 720 = 420
   	12

   
   

   Number of girls =	5	× 720 = 300
   	12

   
   Let x girls be admitted.
   According to the question,
   420 = 300 + x
   ⇒  x = 420 – 300 = 120

   Correct Option: B

   Boys : Girls = 7 : 5
   

   Number of boys =	7	× 720 = 420
   	12

   
   

   Number of girls =	5	× 720 = 300
   	12

   
   Let x girls be admitted.
   According to the question,
   420 = 300 + x
   ⇒  x = 420 – 300 = 120

---

397. 12 monkeys can eat 12 bananas in 12 minutes. In how many minutes can 4 monkeys eat 4 bananas ?

1. 1. 10

   
   
   

   2. 12

   
   
   

   3. 4

   
   
   

   4. 8

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   ⇒  4 × 12 × x = 12 × 12 × 4
   

   ⇒  x =	12 × 12 × 4
   	4 × 12

   
   = 12 minutes

   Correct Option: B

   
   ⇒  4 × 12 × x = 12 × 12 × 4
   

   ⇒  x =	12 × 12 × 4
   	4 × 12

   
   = 12 minutes

---

---

398. What must be added to each term of the ratio 2 : 5 so that it may equal to 5 : 6 ?

1. 1. 65

   
   
   

   2. 78

   
   
   

   3. 13

   
   
   

   4. 12

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let x be added to each term.
   According to the question,
   

   2 + x	=	5
   5 + x		6

   
   ⇒  12 + 6x = 25 + 5x
   ⇒  6x – 5x = 25 – 12
   ⇒  x = 13

   Correct Option: C

   Let x be added to each term.
   According to the question,
   

   2 + x	=	5
   5 + x		6

   
   ⇒  12 + 6x = 25 + 5x
   ⇒  6x – 5x = 25 – 12
   ⇒  x = 13

---

399. If A : B = 2 : 3 and B : C = 3 : 7, then A + B : B + C : C + A is

1. 1. 4 : 8 : 9

   
   
   

   2. 5 : 8 : 9

   
   
   

   3. 5 : 10 : 9

   
   
   

   4. 4 : 10 : 9

   
   
   

---

1. View Hint View Answer Discuss in Forum

   A : B = 2 : 3
   B : C = 3 : 7
   ∴  A : B : C = 2 : 3 : 7
   ∴  A = 2k, B = 3k, C = 7k
   ∴  A + B = 5k; B + C = 10k,
   C + A = 9k
   ∴  Required ratio = 5k : 10k : 9k
   = 5 : 10 : 9

   Correct Option: C

   A : B = 2 : 3
   B : C = 3 : 7
   ∴  A : B : C = 2 : 3 : 7
   ∴  A = 2k, B = 3k, C = 7k
   ∴  A + B = 5k; B + C = 10k,
   C + A = 9k
   ∴  Required ratio = 5k : 10k : 9k
   = 5 : 10 : 9

---

---

400. If (x³ – y³) : (x² +xy +y²) = 5 : 1
     and (x² – y²) : (x – y) = 7 : 1, then the ratio 2x : 3y equals

1. 1. 4 : 1

   
   
   

   2. 2 : 3

   
   
   

   3. 4 : 3

   
   
   

   4. 3 : 2

   
   
   

---

1. View Hint View Answer Discuss in Forum

   x3 − y3	=	5
   x2 + xy + y2		1

   
   

   ⇒	(x − y)(x2 + xy + y2)	= 5
   	x2 + xy + y2

   
   ⇒   x – y = 5       ....(i)
   Again,
   

   x2 − y2	= 7
   x − y

   
   

   ⇒	(x + y)(x − y)	= 7
   	x − y

   
   ⇒   x + y = 7       ....(ii)
   On adding equations (i) and (ii),
   2x = 12 ⇒ x = 6
   From equation (ii),
   x + y = 7 ⇒ y = 7 – 6 = 1
   

   ∴	2x	=	2 × 6	= 4 : 1
   	3y		3 × 1

   Correct Option: A

   x3 − y3	=	5
   x2 + xy + y2		1

   
   

   ⇒	(x − y)(x2 + xy + y2)	= 5
   	x2 + xy + y2

   
   ⇒   x – y = 5       ....(i)
   Again,
   

   x2 − y2	= 7
   x − y

   
   

   ⇒	(x + y)(x − y)	= 7
   	x − y

   
   ⇒   x + y = 7       ....(ii)
   On adding equations (i) and (ii),
   2x = 12 ⇒ x = 6
   From equation (ii),
   x + y = 7 ⇒ y = 7 – 6 = 1
   

   ∴	2x	=	2 × 6	= 4 : 1
   	3y		3 × 1

---