Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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 = $x×y^2$.

Explanation:

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.

Explanation:

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.

Explanation:

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 ).

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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

Explanation:

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.

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

Next number = Previous number + Reverse of previous number

So

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