If SQRT(x+15) + SQRT(x)=15 then find the value of x.

Given x is a real number, If SQRT(x+15) + SQRT(x)=15 then find the value of x.

Solution -

It infers sqrt(x+15)=15-sqrt(x) square both sides
x+15=225+x-30*sqrt(x) or
sqrt(x)=7 or x=49 substitute in the statement o.k.

The ratio between the present ages of Pawan and Rohan is 5:7...............What is the sum of Pawan

The ratio between the present ages of Pawan and Rohan is 5:7 respectively.
If the difference between Rohan’s current age and Pawan’s age after 6 years is 2.
What is the sum of Pawan & Rohan current age?

Solution -

R/P=5/7
R-(P+6)=2 OR R-P=8 Substitute above relation
R-5R/7=8 or 2R/7= 8 giving R=28 and P=20

How many 3 digit numbers can be formed from digits 2, 3, 5, 6, 7 & 0, which are divisible by 5 a

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5 and none of the digits is repeated?

Solution -

Looks 36. Ending with 0 we have to select two others from 5 which means 5P2=20. Similarly ending with 5 we have another 20 of which 4 starting with zero must be excluded. Hence 20+16=36

Simplify 9^2^-1^3^4^5

Simplify 9^2^-1^3^4^5




Solution -

1^3^4^5 = 1
9^2^(-1) = 9^(1/2) = sqrt of 9 = 3.

How much worth chocolate should he buy so that he can accommodate it in Rs 100 ?

Rohit went to buy some expensive, foreign chocolates. He only had Rs 100 with him. When he reached the shop, he got to know that on those chocolates, there was a 15% import duty and 5% VAT.

How much worth chocolate should he buy so that he can accommodate it in Rs 100 ?

Solution -

If the VAT is added on the base price + Import Duty then

He would be able to buy chocolates worth Rs. 82.816

82.816 + Import Duty @ 15% Rs.12.422 = 95.238

Add 5% VAT on 95.238
Rs. 4.762

95.238 + 4.762 = 100

A sum is increased to 40% in 8 years at SI. What will be the compound interest of Rs. 1600 after 3 y

There is 40% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 1,600 after 3 years at the same rate?

Solution -

Simple interest comes 40/8=5 %. Amount from principal of 1600 at 5% for three years becomes 1600*1.05^3=1852.20. Therefore compound interest comes Rs. 252.20

The difference between simple interest and compound interest on a sum for 2 years at 8% is Rs.16...

The difference between simple interest and compound interest on a sum for 2 years at 8%, when the interest is compounded annually is Rs.16. If the interest were compounded half yearly, then what would be the difference between simple interest and compound interest for the same sum in 2 years?

Solution -

the difference between the compound interest and simple interest for 2 yearsmay be arrived in the form PxRXR/10000.
R=8,solving get P=2500
Simple interest for the amount=400
comp interest =416
comp interest half-yearly =424.65
hence difference =24.65

Sum of first six terms of an AP is 42 and ratio of 10th term to its 30th term is 1:3. Calculate fist

Sum of first six terms of an AP is 42 and ratio of 10th term to its 30th term is 1:3. Calculate fist




Solution -

Tn = [a + (n-1)d]
Sn = n/2*[2a +(n-1)d].
Given
T30/T10 = 3
(a + 29d)/(a + 9d) = 3
After simplification we get
a = d

S6 = 6/2 [2a + 5d] = 42 (given)
14 = 2a + 5d
14/7 = 2 = a = d ( substituting a = d)

So the series starts like
2, 4, 6, 8, 10, 12, 14, 16, .......
Now T13 = [2+12d] = [2 + 24] = 26.

If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

If A+B = 225 then what would be (1+tan A)(1+tan B) = ??




Solution -

A+B=225;; A+B=180+45 ;; -45=180-(A+B)  ;;  

TAKING TAN BOTH SIDES ;;; TAN(-45)=TAN(180-(A+B));;; -1=-TAN(A+B);;

                  TAN(A+B)=1 ;;;                    TAN(A) + TAN(B) = 1- TAN(A)TAN(B) ;;;                    TAN(A)+TAN(B)+TAN(A)TAN(B) = 1 ;;             Question was to find {1+TAN(A)}{1+TAN(B)} === 1+ TAN(A) +TAN(B) + TAN(A)TAN(B)  == 1+ 1 == 2  

What is the probability of 2 people having the same number of body hair in the world ?

Assuming a person can grow a maximum of 40 crore hair on thier body and that the world has a population of 730 crore, What are the chances of 2 people having the same number of body hair on them ?

Solution -

Looks 1/40 crore. Let the first person grow any number say n of hair. Second person can be anybody growing any number from 1 to 40 crore. The probability of n appearing in 40 crore is 1/40 crore.

What would be the probability that leap year would have exactly 52 Tuesdays?

What would be the probability that leap year would have exactly 52 Tuesdays?




Solution -

The probability here as asked "exactly"
Is actually this
Now , as we know that a leap year has 366 days
This means if we want to have exactly 52 Tuesdays then the remaining two days must not be a Tuesday
The outcomes can be either
(Sun,Mon) (Mon,Tues),(Tues,wed) (Wed,thurs) (thurs,fri) (fri,sat)
(Sat,sun) .now the favourable outcomes are only 5 , therefore it should be 5/7
It is 5/7

What would be the sum of all 3 digit number formed by using digits 3, 4, 6 & 8, with no digit is

What would be the sum of all 3 digit number formed by using digits 3, 4, 6 & 8, with no digit is




Solution -

Nevertheless I have used a spread sheet to find the 4P3 i.e. 24 three digit numbers. Each column has any digit 6 times. Hence the total of any column is 6*(3+4+6+8) i.e. 126. Writing 6 in the unit place we carry 12 to the second column which again has a total of 126 which makes it 126+12=138. We write 8 in the tens place and carry 13 to the third column. The third column will be 126+13=139 which we have to write as it is. Hence the answer reads 13986.

If twice the numerator is 2 more than the denominator and if 3 is added to each, new fraction is 2/3

In a rational number,
twice the numerator is 2 more than the denominator.
If 3 is added to each i.e. the numerator and the denominator, the new fraction is 2/3.

Find the original number?

Solution -

let the numerator be a and the denominator b. One of the equations is 2a=b+2. The other equation is (a+3)/b+3)=2/3. The solution gives a=7 and b=12. First check 2*7=12+2. Second check (7+3)/(12+3)=2/3

What is the ratio of their speeds?

Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively.
What is the ratio of their speeds?

Solution -

Let the distance between Howrah and Patna be D kilometer and let the trains cross at a distance of x from Howrah. Let us call the train from Howrah to Patna as T1 and other T2 and their corresponding speeds s1 and s2. The remaining distance in case of first train is D-x and in the other x. Since the first train covers its remaining distance in 9 hours and the other in 16 hours s1=(D-x)/9 similarly s2=x/16............(1)
There fore s1/s2=16*(D-x)/(9*x)
Since the two train cross after equal time from the start, their distances covered are in proportion to their speeds.
This gives s1/s2=x/(D-x).................(2)
From equation (1) and (2)
x/(D-x)=s1/s2=16s2/9s1
Cross multiplying gives s1/s2 = 4/3

Length, breadth & height of a room are in ratio 3:2:1. If the breadth & length are halved, w

If length, breadth and height of a room are in the ratio 3:2:1. If the breadth and length are halved, while the height is doubled. Then what is the percentage change in the total area of the 4 walls of the room?

Solution -