**1. 12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour. **
** Answer**: Option A

**Explanation**:
1 man is equivalent to 2 boys in work capacity. 12 men + 18 boys = 12 x 2 + 18 = 42 boys.
Let the required number of boys be x. So a Total number of people doing work = 21 men x 2 (according to work capacity) + x boys.
Taking respective ratios as required:
Given:
=> Hours 50:60
=> Minutes per hour 9: [latex]\frac{15}2 }[/latex]
=> Work 1:2
=> People: 42: 42 + x
=> 50 x 9 x 1 x (42+x) = 60 x [latex]\frac{15}{2 }[/latex] x 2 x 42
=> 42 + x = 84
x = 42

**2. 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job? **
** Answer**: Option C

**Explanation**:
Solution: It is given that 5/8th of the work is completed in 10 days.
=> Remaining work = [latex]\frac{3}{8 }[/latex]th of total
Applying the unitary method:
Total work will be completed in 10 * [latex]\frac{8}{5 }[/latex] days
=> It takes 16 days to complete total work
=> Hence, remaining work days = 16 - 10 = 6 days

**3. If the ratio of present ages of Jeet and Jay is 5:7 and after 6 years the ratio will be 3:4, what is the present age of Jay? **
A. 42
B. 30
C. 36
D. None of these

** Answer**: Option A

**Explanation**:
As the present age of Jeet and Jay are in the ratio 5:7, let their ages be 5x and 7x respectively.
Therefore, their ages after 6 years will be (5x+6) and (7x+6) respectively.
Now, it is given that [latex]\frac{(5x+6)}{(7x+6) }[/latex] = [latex]\frac{3}{4 }[/latex]
4*(5x+6) = 3*(7x+6)
x = 6
Hence, the present age of Jay is 7x = 7*6 = 42 years

**4. Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2. **
** Answer**: Option A

**Explanation**:
Let z = 4y-1
When x = 14, y = 2, z = (4*2) – 1 = 7
Now, x varies directly as z = 4y-1
When y = 5, z = (4*5) – 1 = 19
x 14 7
y - 19
Therefore, x = [latex]\frac{(14*19)}{7 }[/latex]= 38

**5. In what ratio must one add water to milk so as to gain 16.666% on selling this mixture at the cost price? **
** Answer**: Option A

**Explanation**:
To start off this question let us assume that cost price of 1 litre milk is Rs 1
No need to make a mixture and sell this mixture at 1 Rs per liter such that the total gain on the mixture is 16.667%.
Therefore, CP of 1 liter of the mixture becomes (quantity of milk)/ (quantity of mixture containing 1 L milk)*(the price of 1-liter milk).
=>(100/(100+50/3))*1
=>CP of 1-litre milk of mixture: Rs 5/6
As the price of any amount of water is zero, and as 1-liter milk costs Rs 1.5/6litre of the mixture will comprise entirely of cost of milk which means,1 liter of the mixture will
contain a 5/6th amount of milk.
=>Water is added in the ratio of (1-5/6)=1/6