First number that is divisible by 4 from 432 is 436.

And the last number that is divisible by 4 is 4196.

Therefore, we have to find the number of terms in the series 436, 440,…,4196.

This is an A.P. in which first term = a = 436, common difference = d = 4 and the last term = l = 4196.

Let, tn = l = 4196; then it is enough to find n.

a + (n-1) d = 4196

436 + (n-1) 4 = 4196

(n-1) 4 = 3760

(n-1) = 940.

n = 941.

Hence, the number of natural numbers between 432 and 4200 is 941.

Sum of the age of 25 children = 12.5 x 25

The age of two of them are 8 and 10.

Sum of remaining 23 children = (12.5 x 25) – (8 + 10) = 312.5 – 18 = 294.5

And their average age = 294.5/23 = 12.8

By observing, we can conclude that questions are in the general form X * Y = X+Y / 2 .

That is,

27 x 7 = 27+7 / 2 = 17

37 x 9 = 37+9 / 2 = 23

47 x 11 = 47+11 / 2 = 29

57 x 13 = 57+13 / 2 =70/2 = 35.

Hence, the answer is 35.

Let the speed of the stream be X km/hr.

Then speed in downstream = (5+X) km/hr

And, speed in upstream = (5-X) km/hr

The time taken to cover 7 km upstream = 7/(5-X)

13(5-X) = 7(5-X)

65 – 13X = 35+7X

30 = 20X

X = 30/20 = 3/2

Discount on marked price = 3%

ie., S.P = 97/100 x 65000 = Rs.(97 x 650) = Rs.63050

i.e., if the S.P is Rs.130 then its C.P = Rs.100

Therefore the C.P of the bike = Rs. 100/130 x 63050 = Rs.(100×485) = Rs.48500

Hence the required answer is Rs.48500.

Actual share of each = Rs.1904/8 = Rs.238

If one of 8 is left, then the sharing amount = Rs.1904/7 = Rs.272

Then the extra amount given by each = Rs.(272 – 238) = Rs.34.

Hence the answer is Rs.34

Since the number 95478 end with 8, discard it.

i.e., the prime factors are 2, 3, 7 and their powers are even numbers.

Therefore, 63504 is a perfect square.

Length and breadth of the room are 30m and 24m respectively.

Area of the floor = 30 x 24 = 720 m

Twice of the area of the floor = 720 x 2 = 1440 m

Then, length of the wall = h m.

And, the breadth of the 4 walls = 30m, 24m, 30m and 24m respectively.

Area of the other two opposite walls with breadth 24 m and height h m = 2(24h) m

Sum of the areas of four walls = 2(30h) + 2(24h) = 2h(30 + 24) = 108h m

1440 = 108h

h = 1440/108 = 40/3 m.

Hence the answer is 9600 m

And, they are moving in the opposite direction, they take 25 seconds to cross each other.

Now, from the formula (a + b)/(u + v), we have a = b = 250 m and u = v = X m/sec.

25 = 500/2X sec.

X = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.

Hence, the speed of two trains is 36 km/hr.

Let r and 2r be their radius.

Let h and 3h be their respective heights.

(1/3) (pi) (r

(1/3) (pi) (2r)

(1/3) (pi) (r

= 1/12

Hence the required ratio is 1:12.

X = 10100 – 5% of 10100 – 48.4% of 9500

X = 10100 – 5×10100/100 – 48.4×9500/100

X = 10100 – 5×101 – 48.4×95

X = 10100 – 505 – 4598 = 4997.

3rd number: 2nd x 2 = 19.5 x 2 = 39

4th number: 3rd x 2.5 = 39 x 2.5 = 97.5

5th number: 4th x 3 = 97.5 x 3 = 292.5

6th number: 5th x 3.5 = 292.5 x 3.5 = 1023.75 (note that, there is 1028 instead of 1023.75).

We have to find the difference of cost of wheat and pulses; i.e., X – Z.

Average cost of rice and wheat = Rs.(X+Y) / 2

Average cost of wheat and pulses = Rs.(Y+Z) / 2

Given that, Rs.(X+Y) / 2 – Rs.(Z+Y) / 2 = Rs.30

(X + Y) – (Z + Y) = Rs.60

(X – Z) = 60.

Hence, the answer is Rs.60.

4th number = 5th number x 2 + 2 = 81 x 2 + 2 = 164

3rd number = 4th number x 2 + 3 = 164 x 2 + 3 = 331

2nd number = 3rd number x 2 + 4 = 331 x 2 + 4 = 666 (there is 662 instead of 666).

1st number = 2nd number x 2 + 5 = 666 x 2 + 5 = 1337.

Therefore, 2nd number 662 is the wrong number.

Then, product of the numbers = 19 x 1140

Let 19a and 19b be the numbers.

19a x 19b = 19 x 1140

ab = 19 x 1140 / 19 x 19 = 60

Since a and b are co-primes then (a,b) = (1,60), (4,15) and (5,12)

Hence the number of such pairs = 3a

i.e., lowest number which divisible by 7, 10, 16 and 28 is 560.

Then the lowest number which leaves 6 when divided by 7, 10, 16 and 28 is 560 + 6

Therefore the lowest multiple of 6, leaving 6 as remainder when divided by 7, 10, 16 and 28 is 560k + 6

If k = 1, 560k + 6 = 560 + 6 = 566 which is not a multiple of 6

If k = 2, 560k + 6 = 1120 + 6 = 1126 which is not a multiple of 6

If k = 3, 560k + 6 = 1680 + 6 = 1686 which is a multiple of 6.

Hence the required least number is 1686.