A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

Correct Answer: 450

Explanation:

Let the required no of hectares be x. Then 

More men, More hectares      (Direct proportion)

More days, More hectares      (Direct proportion)

  M e n 8 : 36 D a y s 24 : 30 ? ? 80 : x

=> ( 8 * 24 * x) = (36 * 30 * 80)

=>  x= 450

Correct Answer: Rs. 340

Explanation:

Assume first child (the youngest) get = Rs. x

According to the question ;
each son having Rs. 30 more than the younger one

Second child will get = Rs. x + 30
Third child will get = Rs. x + 30 + 30 = x + 60
Forth child will get = Rs. x + 30 + 30 + 30 = x + 90
Fifth child will get = Rs. x + 30 + 30 + 30 + 30 = x + 120

Total amount they got = Rs. 2000

x + (x+30) + (x+60) + (x+90) + (x+120) = 2000
5x + 300 = 2000
5x = 1700
x = Rs. 340
So the youngest child will get Rs. 340.

Correct Answer: 14

Explanation:

1 2 3 4 5 6(Shankar) 7(Nitu) 8(Althaf) 9 10 11 12 13 14
Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them
So minimum no. of boys standing in the queue = 14

Correct Answer: 3 days

Explanation:

Let x men can do the in 12 days and the required number of days be z

 

More men, Less days     [Indirect Proportion]

 

Less work, Less days     [Direct Proportion  ]

  m e n 2 x : x w o r k 1 : 1 2 : : 12 : z

? 2 x × 1 × z = x × 1 2 × 12

  ? z = 3

Correct Answer: 12th element

Explanation:

If we consider the third term to be ?x?
The 15th term will be (x + 12d)
6th term will be (x + 3d)
11th term will be (x + 8d) and
13th term will be (x + 10d).
Thus, as per the given condition, 2x + 12d = 3x + 21d.Or x + 9d = 0.
x + 9d will be the 12th term.

Thus, 12th term of the A.P will be zero.

Correct Answer: Rs. (yd/x)

Explanation:

Cost of x metres = Rs. d.

Cost of 1 metre = Rs.(d/x)

Cost of y metres = Rs.[(d/x).y] = Rs.(yd/x)

Correct Answer: 48 Paise

Explanation:

Let the Required cost be X paise.  Less Weight , Less cost (Direct Proportion)

Therefore, 250 : 200 :: 60 : x

=> (250 * x) = (200 * 60)

=> x= 48

Correct Answer: 40

Explanation:

Let the required number of days be x.

 

Less cows, More days (Indirect Proportion)

 

Less bags, Less days (Direct Proportion)

 

$$\begin{gathered} c o w s 1 : 40 : 40 : x \\ b a g s 40 : 1 : 40 : x \\ \end{gathered}$$

 

1 x 40 x x = 40 x 1 x 40

 

=>  x = 40.

Correct Answer: 16

Explanation:

Let the required number of bottles be x.

 

More weavers, More mats (Direct Proportion)

 

More days, More mats (Direct Proportion)

 

 

$$\begin{gathered} w e a v e r s 4 : 8 } : 4 : x \\ d a y s 4 : 8 } : 4 : x \end{gathered}$$ 

4 x 4 x x = 8 x 8 x 4

 

=> x =  8 * 8 * 4 4 * 4

 

=> x = 16.

Correct Answer: 6 hours a day

Explanation:

More Men, Less Hours {Indirect Proportion}

Less Days, More Hours {Indirect Proportion}

  m e n 15 : 10 d a y s 12 : 18 ? ? 6 : x

 

=> 15 * 12 * x = 10 * 18 * 6

=>x = 6