835 - 16 = 819
819 - 18 = 801
801 - 20 = 781
781 - 22 = 759
So, the next term is 759 - 24 = 735

The first term is 85.
2nd term = 85 - 1 = 84.
3rd term = 84 + (-1)² = 85
4th term = 85 - 2 = 83
5th term = 83 + (-2)² = 87

So, the last term in the series is 91 + (-8)² = 91 + 64 = 155

In the above series,

2nd term = 1st term * 2 + 1
3rd term = 2nd term * 2 + 1
and so on.

So, the 5th term in the series = 127*2 + 1 = 255

The n^th  term of the above series is n² + 1. So, the 1st term is 1² + 1 = 2, the 2nd term is 2² + 1 = 5. The third term is 3² + 1 = 10 and so on. So, the 6th term is 6² + 1 = 37.

The first term is 25. The second term is 25*3 + 1. The third term is 25*5 + 2. The fourth term is 25*7 + 3 and so on. So, the next term in the series will be 25*11 + 5 = 280.

Let the prices of apples, mangoes and bananas be represented by a, m and b. So we have
5a + 3m + 2b = 43
4a + 2m + b = 31
7m + 4b = 40
Multiplying equation 1 by 4 and 2 by 5 and then subtracting them we get
2m + 3b = 17
Now solving this and third equation we get
m = 4 and b = 3
Hence, a = 5
Thus, required answer = 5 + 4 + 3 = 12.

The resultant time take when the pipe fills with the hole emptying the tank is :

Let us assume the total number of students in the school to be 120.
Number of boys: Number of girls = 7:5.
=> Number of boys = 70
Number of girls = 50

30% of the total students play cricket.
Therefore, 30% of 120 = 36 students play cricket in total.
50% of the boys play cricket.
Number of boys who play cricket = 0.5*70 = 35.
=> Number of girls who play cricket = 36 - 35 = 1.
Percentage of girls who play cricket = 1/50 = 2%.

The speed of the boat while travelling downstream = 16 km/hr and while travelling upstream = 24 km/hr. Let the distance between Allahabad and Varanasi be D.
We have
D/16 + D/24 = 15
=> (3D + 2D)/48 = 15
=> 5D = 720
=> D = 144 km.

Let’s say A and B are 3x , 2x
So 24x^2 = 540 + 9x^2
On solving above equation we will get x=6
Hence 3x=18 and 2x=12