171. Seventy-five men are employed to lay down a railway line in 3 months. Due to certain emergency conditions, the work was to be finished in 18 days. How many more men should be employed to complete the work in the desired time ?

1. 1. 300

   
   
   

   2. 325

   
   
   

   3. 350

   
   
   

   4. 375

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   M₁D₁ = M₂D₂
   ⇒ 75 × 90 = M₂ × 18
   

   ⇒ M2 =	75 × 90	= 375
   	18

   
   7there4; Number of additional men
   = 375 – 75 = 300

   Correct Option: A

   Using Rule 1,
   M₁D₁ = M₂D₂
   ⇒ 75 × 90 = M₂ × 18
   

   ⇒ M2 =	75 × 90	= 375
   	18

   
   7there4; Number of additional men
   = 375 – 75 = 300

---

172. If 4 men or 8 women can do a piece of work in 15 days, in how many days can 6 men and 12 women do the same piece of work ?

1. 1. 20 days

   
   
   

   2. 45 days

   
   
   

   3. 15 days

   
   
   

   4. 30 days

   
   
   

   5. None of these

   
   
   

---

1. View Hint View Answer Discuss in Forum

   4 men ≡ 8 women
   ⇒ 1 man ≡ 2 women
   ∴ 6 men + 12 women ≡ 12 women + 12 women ≡ 24 women
   ∴ M₁D₁ = M₂D₂
   ⇒ 8 × 15 = 24 × D₂
   

   ⇒ D2 =	8 × 15	= 5 days
   	24

   
   Aliter : Using Rule 12,
   Here, A = 4, B = 8, a = 15
   A₁ = 6, B₁= 12
   Required number of days
   

   =	a(A × B)
   	A1B + B1A

   
   

   =	15 × 32	= 5 days
   	96

   Correct Option: E

   4 men ≡ 8 women
   ⇒ 1 man ≡ 2 women
   ∴ 6 men + 12 women ≡ 12 women + 12 women ≡ 24 women
   ∴ M₁D₁ = M₂D₂
   ⇒ 8 × 15 = 24 × D₂
   

   ⇒ D2 =	8 × 15	= 5 days
   	24

   
   Aliter : Using Rule 12,
   Here, A = 4, B = 8, a = 15
   A₁ = 6, B₁= 12
   Required number of days
   

   =	a(A × B)
   	A1B + B1A

   
   

   =	15 × 32	= 5 days
   	96

---

---

173. 24 men can do a piece of work in 17 days. How many men will be able to do it in 51 days ?

1. 1. 8

   
   
   

   2. 10

   
   
   

   3. 12

   
   
   

   4. 6

   
   
   

---

1. View Hint View Answer Discuss in Forum

   M₁D₁ = M₂D₂
   ⇒ 24 × 17 = M₂ × 51
   

   ⇒ M2 =	24 × 17	= 8 men
   	51

   Correct Option: B

   M₁D₁ = M₂D₂
   ⇒ 24 × 17 = M₂ × 51
   

   ⇒ M2 =	24 × 17	= 8 men
   	51

---

174. Suman can do a work in 3 days. Sumati can do the same work in 2 days. Both of them finish the work together and get ₹ 150. What is the share of Suman ?

1. 1. ₹ 30

   
   
   

   2. ₹ 60

   
   
   

   3. ₹ 70

   
   
   

   4. ₹ 75

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Ratio of Suman’s and Sumati’s 1 day’s work
   

   =	1	:	1	= 2 : 3
   	3		2

   
   Sum of the ratios = 2 + 3 = 5
   

   Suman’s share =	2	× 150 = ₹ 60
   	5

   
   Aliter : Using Rule 24,
   Here, m = 3, n = 2, R = 150
   

   Share of suman =	n	× R
   	m + n

   
   

   =	2	× 150 = 60
   	3 + 2

   Correct Option: B

   Ratio of Suman’s and Sumati’s 1 day’s work
   

   =	1	:	1	= 2 : 3
   	3		2

   
   Sum of the ratios = 2 + 3 = 5
   

   Suman’s share =	2	× 150 = ₹ 60
   	5

   
   Aliter : Using Rule 24,
   Here, m = 3, n = 2, R = 150
   

   Share of suman =	n	× R
   	m + n

   
   

   =	2	× 150 = 60
   	3 + 2

---

---

175. The average wage of 500 workers was found to be ₹ 200. Later on, it was discovered that the wages of two workers were misread as 180 and 20 instead of 80 and 220. The correct average wage is :

1. 1. ₹ 200.10

   
   
   

   2. ₹ 200.20

   
   
   

   3. ₹ 200.50

   
   
   

   4. ₹ 201.00

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Total wages of 500 workers
   = 500 × 200 = ₹ 100000
   Now, according to question, Correct Average
   

   =	100000 - 180 - 20 + 80 + 220
   	500

   
   

   =	100100	= ₹ 200.20
   	500

   Correct Option: B

   Total wages of 500 workers
   = 500 × 200 = ₹ 100000
   Now, according to question, Correct Average
   

   =	100000 - 180 - 20 + 80 + 220
   	500

   
   

   =	100100	= ₹ 200.20
   	500

---