If a,b,c are the three sides of the triangle.

Then formula for Area = (s(s-a)×(s-b)×(s-c))−−−−−−−−−−−−−−−−−−−√(s(s-a)×(s-b)×(s-c))

Where s = (a+b+c)2=12×(30+c)(a+b+c)2=12×(30+c)

[Assume a = 20 ,b = 10]

Now,

Check the options.

From the 1st statement b is even, as when multiplied by odd it gives even

a2a2 - b = even

=> a is even

Here none of a and b are odd.

Let additional weight on left arm be x.

Weight of melon be m

x + 1 = 8 x m - - - - - - (1)

x + 2 x m = 1 - - - - - - (2)

Solving 1 & 2 we get.

Weight of a single Melon = 200 gm.

Observe that each letter appeared once, twice, thrice .... They form an arithmetic progression. 1+2+3......

We know that sum of first n natural numbers = n(n+1)2n(n+1)2

So n(n+1)2n(n+1)2 ≤≤ 288

For n = 23, we get 276. So for n = 24, the given series crosses 288.

Ans is X.

ABC = C3C3

So, look for a number, that has a 3 digit cube, and the last digit of the cube is same as the number itself:

5353 = 125

So, CAB = 512 = 8383

D = 8 and B = 2

83÷2383÷23

Answer = 64.

Work done in 1 min =10 + 403403 - 5= 553553 kg/min

For 1 kg = 3/55 min

For 2.4 tonnes = 3/55 x 2.4 x 1000 = 130 mins = 2hrs 10min.

A=$x^3×y^2x^3×y^2$

B = $x×y^3x×y^3$

To find the HCF of the above numbers, take minimum power of x and y in both the numbers.

HCF = Common terms from both A & B and minimum powers = $x×y^2$.

HERE = COMES - SHE

HERE

+ SHE

COMES

E + E = S = 8 => E = 4

3 digit no. + 4 digit no. = 5 digit no. => C = 1 ,O = 0, H = 9 etc

So 9454 + 894 = 10348

10348

- 894

9454

R + H + O = 5 + 9 + 0 = 14.

He must have born in BC 570

Hence in BC 500 he will be 70 years

And in BC 490 he will be 80 years.

The question basically states that if Lucia were to have say 10 sons, then each son would have 9 sons (Lucias grandsons - since each son has 9 brothers). So the total in this case would be 9××10 grandsons + 10 sons = 100.

Let us assume Lucia has got x sons. Now each son has (x - 1) sons. So total = x + (x - 1) x. For x = 8 we get 64 which is in between 50 and 60. ( 7 x 8 grandsons + 8 sons = 64 ).

Clearly 11 mornings and 12 afternoons = 23 half days

since 13 days raining means 13 half days.

so 23 - 13 =10 half days ( not affected by rain )

so 10 half days = 5 full days

Total no. of days = 13 + 5 = 18 days.

Prime number up to 50 are

2,3,5,7,11,...,43,47

Product = 2×3×5×7×11×−−−×43×472×3×5×7×11×−−−×43×47

Theres a term 2×5=102×5=10

So unit digit of product = 0.

HOW

+ MUCH

POWER

Here p = 1 and M = 9 because after adding carry bit it gives result 10. Hence O = 0,here three digits 0,1,9 have been used.

Now, put all remaining value in 3rd column and check which value is suitable for H,U and W and we get H = 7,U = 8 and W = 5 and 1 carry which will be added in 4th column.

Now in first column we have W + H = R means 5 + 7 = 2 and 1 carry will add in 2nd column in 2nd column, 0 + C = E,0 + 3 + 1 = 4 so C = 3,E = 4

Therefore,

9837

+ 705

10542

so P + O + W + E + R = 1 + 0 + 5 + 4 + 2 = 12.

It follows the series as:

1 x 2 = 2

2 x 1 = 2

3 x 4 = 12

4 x 3 = 12

5 x 6 = 30

6 x 5 = 30

7 x 8 = 56

This is the required number for the series.

71.8 = (71x+73y)/(x+y)?

71.8 (x+ y) = 71x + 73y

0.8x = 1.2y

x:y = 12:8 which is equals to 3:2

If C and D form a pair and A and B form a pair the difference is maximum.

Now C and D together can complete the work =$\dfrac{9\times18}{9+18}$

A and B together can complete the work = $\dfrac{2\times 4}{2+4}$

Difference = 6 - 4/3 = 14/3 days.

Total number of 4 digit numbers are 9000 (between 1000 and 9999).

We find the numbers without any two in them. So total numbers are 8 x 9 x 9 x 9 = 5832

So numbers with number two in them = 9000 - 5832 = 3168

Total 3 digit numbers = 9 x 10 x 10 = 900

Total number of 3 digit numbers without repetition = 9 x 9 x 8 = 648

So number of three digit numbers with at least one digit repeats = 900 - 648=252

S.P. of 1 kg mixture = Rs.23. Gain = 15%.

C.P. of 1 kg mixture = Rs.[(100/115) x 23] = Rs.20

Let the quantity of wheat costing Rs.24 is x kgs.

Using weighted average rule = $\dfrac{x\times24+30\times18.4}{x+30}$ = 20

Solving we get x = 12

Next number = Previous number + Reverse of previous number

So

7 ,7+7=14, 14+41 = 55, 55+55 = 110, 110+011 = 121