Gita can do a piece of work in 3 days which can done by sita in 4 days .if sita can do a piece of work in 5 days which can done by rita in 6 days ,,in how many dayd will gita can do a work can be done by rita 16days?

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The sum of the digits of two-digits number is 10. If 18 is added to the number , its digits are reversed. Find the number.

Soln:
Let the two digits number = 10x +y where
tens place digit = x
units place digit = y
according to the first condition
x+y = 10................(1)
according to the second condition
10x + y + 18 = 10y + x
or, 10x- x + y -10y = -18
or, 9x - 9y = -18
x - y = -2..............(2)
solve the equestion 1 & 2 we get
x + y = 10
x - y = -2
´´´´´´´´´´´´´´´´´´´´´´´´
2x = 8
or, x = 4
put the value of x in equation (1) we get
4 + y = 10
or, y = 10 - 4
or, y = 6
so the two-digites number = 10x + y
= 10 × 4 + 6
= 46 Ans.

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The sum of present ages of a brother and his younger sister is 16 years . If the product of their ages is 63. Find their ages.

soln: 
Let the present age of brother = x
and the present age of sister = y
according to the first condition
x + y = 16
or x = 16 - y .......(i)
according to the second condition
xy = 63.........(ii)
solving the equation (i) & (ii), we have,
(16 - y)y = 63
or, 16y - y^2 = 63
or, y^2 - 16y+63 = O
or, y^2 -9y - 6y + 63 = o
or, (y-9)(Y-7) = 0
or, (y - 9) = o
or, y = 9
put the value y in equation (i), we get
x =16 - 9
= 7
so, present age of brother = x = 7 years
and the present age of sister = y = 9 years

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The sum of the ages of the father and son is 44 years. After 8 years, the age of the father will be twice the age of the son. Find their present ages.

Soln:
Let the present age of father = x years
and the present age of son = y years
according to the first condition 
x + y =44 ........(i)
according to the second condition
x+8 = 2(y+8)
or x+ 8 = 2y + 16
or x- 2y = 8 ............(ii)
solve the equation (i) & (ii) we get
x + y =44
x- 2y = 8
••••••••••••••••••••••••
3y = 36
or y = 12
put the value of y in equation (i), we get
x + 12 =44
or x = 32
so the present age of father = x =32 years
and the present age of son = y = 12 years.

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If A+B+C=pi , prove that: sin5A+sin5B+sin5C=4cos(5A/2).cos(5B/2).cos(5C/2)

Soln:

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Q. If a sum becomes Rs. 6480 in 3 years and Rs. 7776 in 4 years, interest being compounded annually, find the sum and rate of interest.

Soln:

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Bibha said to Bigyata," I'm twice as old as you were when I was as old as you are.". If the sum of their present age is 35 years. Find the present ages.

Soln:

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In a cirlce having radius 7 cm, a tangent 25 cm far from the centre is drawn. What is the length of tangent? Find it.

Soln:
use pythagoras theorem in triangle AOB (h^2 = p^2 + b^2)
OB^2 = OA^2 + AB^2
AB^2=25^2-7^2=576
AB=24

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In the given figure, O is the center of the circle. If ABOC is a rhombus, find the value of angle BAC.

Soln:
if angle BOC=x then reflex angle BOC=360-x
now angle BAC=(1/2) reflex angle BOC=180-x/2
then
angle BAC=angle BOC
x=180-x/2
x=120
so 
angle BAC=180-120/2=120

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If three children are born in a family, calculate the probability that all children are girls by drawing a tree diagram.

Soln:

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A card is drawn randomly from the pack of 52 cards and a dice is thrown once. Determine the probability of not getting a club or not getting 6 on the dice.

Soln:
probability that it will not be a club = 39/52 = 3/4
probability that it will not be 6 in the dice = 5/6

probability of not getting a club or not getting 6 on the dice = (3/4)*(5/6) = 5/8

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A card is drawn randomly from the pack of 52 cards, find the probability of getting neither a king nor an ace.

Soln:
probability that the drawn card will be either king or an ace is 4/52 + 4/52 = 2/13
probability that it will neither be king nor ace is 1-2/13 = 11/13

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In a survey one third of children like only mango and 22 don't like mango at all.Also,2/3 children like orange but 12like none of these -show in venn diagram. -how many children like both types of fruits.

Soln:

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The volume of the combined solid made up of cylinder of height 80cm and hemisphere whose radius is equl to that of cylinder is 2707cm^3. Find the Total Surface Area.

Soln:

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n is an integer from 1 to 50, what is the probability that n(n+1) is (a) a multiple of 5? (b) a multiple of 6?

Soln:

For the number n(n+1) to be divisible by 6 means it should be divisible by 2 and 3 both.

n(n+1) is always divisible by 2 if n is integer.

Now, n(n+1) should be divisible by 3 for that either n should be multiple of 3 or n+1 should be multiple of 3.

So, till 50 the numbers such that n will be multiple of 3 are 3 6 9.........48 = 16 numbers

Similarly, n+1 will be divisible by 3 if n = 2 5 8 ...............50 = 17 numbers, there are no numbers in common.

So, total favourable items will be 16 + 17 = 33 and total possible items are 50 hence probability is 33/50.

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Simplify: a/(1-2a) + a/(1+2a) + 2a/(1+4a^2) + 16a^3 /(16a^4-1)

Soln:

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In the survey between 54 peoples the ratio of playing football and volley ball is 5:4.18 people like both games from venn diagram find the number of people who play football. One person should like one games.

Soln:

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Simplify:

Soln:

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P, Q, R is the midpoint of sides, AS perpendicular to BC. Prove that PQRC is cyclic quadrilateral.

Soln:

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After 10% deviation of Nepali money, $2000 can be exchanged by Rs. 231000. Find the initial exchange rate.

Soln:

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