**1. If [latex]\frac{x}{y}[/latex] = [latex]\frac{3}{4}[/latex] and 8x + 5y = 22, then find the value of x.**
**Answer**: Option D

**Explanation**:
Y = [latex]\frac{4}{3}[/latex] X
Substitute this value in 8x + 5y = 22
8x + 5 [latex]\frac{4}{3}[/latex] x = 22
44x = 66
x = 1.5

**2. The population of city A which is 68000 decreases at the rate of 1200/year. The population of city B which is 42000, increases at the rate of 800 per year. Find in how many years, the population of cities A and B are equal? **
A. 9 years
B. 10 years
C. 13 years
D. 15 years

**Answer**: Option C

**Explanation**:
We have to find the population of cities A and B after x years.
Step 1: Population of city A = 68000, decreases at the rate of [latex]\frac {1200}{year}[/latex]
68000 – 1200x
Step 2: Population of city B = 42000, increases at the rate of [latex]\frac {800}{year}[/latex]
42000 + 800x
Step 3: Find how many populations of cities A and B are equal.
Population of city A = Population of city B
68000 – 1200x = 42000 + 800x
68000 – 42000 = 1200x + 800x
26000 = 2000x
x = 13

**3. A contractor pays Rs. 20 to a worker for each day and the worker forfeits Rs. 10 for each day if he is idle. At the end of 60 days, the worker gets Rs. 300. Find for how many days the worker was idle?
**
A. 28 days
B. 30 days
C. 34 days
D. 40 days

**Answer**: Option B

**Explanation**:
Step 1: Number of days worked by the worker = 60 and he remained idle for x days. Therefore, number of days worked = (60 – x)
Step 2: Each day he was getting paid Rs. 20. Therefore, the payment received for working days = (60 – x) 20
Step 3: After subtracting the amount which he forfeited, he receives Rs. 300.
Therefore,
(60 – x) 20 – 10x = 300
1200 – 20x – 10x = 300
900 = 30x
x = 30 days

**4. On a farm, along with 50 hens, there were 45 goats and 8 horses and some farmers. If a total number of feet be 224 more than the number of heads, then find the number of farmers. **
**Answer**: Option B

**Explanation**:
Let’s the number of farmers be y.
Step 1: Find number of heads
= (50 hens + 45 goats + 8 horses + y farmers)
= (103 + y)
Step 2: Number of feet
= [(Hens 2 × 50) + (45 × 4) + (8 × 4) + (y × 2)]
= [100 + 180 + 32 + 2y]
= 312 + 2y
Step 3: Find number of farmers
(312 + 2y) – (103 + y) = 224
312 + 2y – 103 – y = 224
y = 15
Number of farmers = 15

**5. An express train runs at an average speed of 27 km/hr including the time of stoppage at stations. Another train runs at an average speed of 41 km/hr excluding the stoppage time at stations. Find how many minutes does a train stop in 1 hour. **
A. 20.52 min
B. 15.23 min
C. 12.50 min
D. 10.75 min
E. None of these

**Answer**: Option A

**Explanation**:
Train 1: Travels at an average speed of 27 km/hr
Train 2: Travels at an average speed of 41 km/hr
Therefore, train 1 lags train 2 by (41 – 27) km i.e. 14 km.
Now, we have to find the time, train 2 stops in 1 hour.
We know, Speed = [latex]\frac {Distance}{Time }[/latex]
We know, Distance = 14 km, speed = 41 km/hr
Therefore, Time = [latex]\frac {Distance}{Speed}[/latex]
= [latex]\frac {14}{41}[/latex] = 0.342 hr
Answer is in minutes, hence multiply by 60
0.342 hr = 0.342 x 60 = 20.52 min