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A employee suffers 25 % cut in his salary. By what percent his reduced salary should increase so that he regains his original salary?
Original salary =100
After reduction salary = 75
Increment should be Rs. 25 for regaining the original salary
% increase 75 × x/100 = 25
x = 100/3 = 33 1/3 %
The product of two consecutive even numbers is 1088. Find the lowest number among them.
Numbers be x and x + 2
x(x + 2) = 1088
x2 +2x - 1088 =0
x2+ (34 – 32)x -1088 =0
x(x+34) - 32(x + 34) = 0
(x+34) (x – 32) = 0
So x = 32
x+2 = 34
One child was playing with a thread of 44 cm. First he made a circle with that thread and after that he made a square with the same thread. Find the difference between the area of circle and square?
Length of thread = Circumference of circle = Perimeter of square
Circumference of circle = 2πr = 44
2 x r x 22/ 7 = 44
R = 7
Area of circle = 22/7 x 7 x 7 =154 sq cm
Perimeter of square 4 × side = 44
Side = 11
Area = 11 × 11 = 121 sq cm
Difference = 154 – 121 = 33 sq cm
If 2 cos2θ – 1 = 0 then value of tan2 θ + cot 2θ =? Where θ is less than 90◦
2 cos2θ -1 = 0
cos2θ =1 /2
cosθ =1/√2
cos θ = cos 45◦
θ = 45◦
tan2 45 + cot 245 = (1) 2+ (1) 2 =2
The sum of two digit of a number is 7 if 9 is added to the number the digits get interchanged. Find the original number.
Let the number = 10y + x
10y + x + 9 = 10x +y
9x – 9y = 9
x – y = 1
x + y =7
2x = 8
x = 4
y = 7 – 4 = 3
Original number= 10 × 3+ 4 = 34
A factory produced 1858509 toys in the month of January, 7623 more toys produced in the month of February and owing to short supply of electricity 25838 less toys produced in march. What is the total production in three month?
Jan = 1858509
Feb = 1858509 + 7623 = 1866132
March = 1866132 – 25838 = 1840294
Total = 1858509 + 1866132 + 1840294 = 5564935
Aryan invested 13,500 in fixed deposit in a bank. How much amount will he get on maturity if he invested it at 20 % per annum compound interest for six months compounded quarterly?
Time = 6 months = 2 quarters
Rate of interest = 20 p. a = 20/4 = 5% p. a
Amount = 13500 (1+ 5/100)2
= 13500 × 21/20 × 21/20
= 14883.75
Simplify the following 343 ÷ (7 1/2)4 ÷ 7 x 49 =?
343 ÷ (7 1/2)4 ÷ 7 x 49
= 343 ÷ (7)2 ÷ 7 x 49
= 343 ÷ (7)3 x 49
= 343 x49 / 7 x 7 x7
= 49
When the altitude of the sun changes from 45° to 30°. The shadow of the tower becomes 30 meters longer. Find the height of the tower?
In ∆ ABC
Tan 450 = AB/BC=h/x
Tan 450 = 1
1 = h/x
h = x
In ∆ ABD
Tan 450 = AB/BD=h/(x+30)
Tan 450 = 1/(√3)
1/(√3)= h/(x+30)
tan 45◦ = AB/BC = h/BC
1 = h/BC
h = BC
tan 30◦ = 1/√3
1/√3 = h/x + 300
BD = √3 h
h = x + 30 / √3
BC + CD = √3 AB
AB + 30=√3 AB
AB= 30/(√3 -1 )
AB= 30 /(√3 -1 ) x (√3 +1 )/(√3 +1 )
AB = 30 (√3 +1 )/2
AB = 15 (√3 +1 )
Four Contactors names A, B, C and D started a business in partnership. A has 18 workers that work for 4 months, B has 25 workers that work for 2 months, C has 28 workers that work for 5 months and D has 21 workers that work for 3 months. If A got Rs. 7200 then what is total profit?
Ratio A : B : C : D = 18 × 4 : 25 × 2 : 28 × 5 : 21 × 3
= 72 : 50 : 140 : 63
Total = 325 x
Given 72 x= 7200
x = 100
So total profit = 325 × 100 = 32500
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