Ques 1.
A merchant has 100 kg of rice , part of which he sells at 10% and the rest at 20% profit. If he gains 15% on the whole , the amount sold at 10% profit is ?
Solution :
10 20
15
5 5
Ratio = 5:5=1:1
Amount of rice sold at 10% profit = 1/2 *100= 50 kgs
Ques 2.
The angle made by the x + √3y -6 = 0 with positive direction of x-axis is ?
Solution :
==> √3y = 6 - x
==>y = 6/√3 - 1/√3x
Y = Mx+C
M = -1/3
Tan θ = -1/3
==> -Tan θ =Tan (180-30) = Tan 150
==>θ = 150
Ques 3.
If secθ = 13/5 , then what is the value of (2sinθ -3cosθ )/(4sinθ -9cosθ ) = ?
Solution :
==> sec^2 θ = 169/25
==>1+ tan^2 θ = 169/25
==>tan^2 θ = 144/25
==>tan θ = 12/5
(2sin θ -3 cos θ )/(4sinθ -9cosθ ) = (2 tan θ-3)/(4tan θ-9)
Ques 4.
If ratio of the areas of two square is 225:256 , then the ratio of their perimeter is
Solution :
(a1/a2)^2 = 225/256
==> a1/a2 = 15/16
Ratio of perimeter = 4a1/4a2 = a1/a2 = 15:16
Ques 5.
If 3x^3 - 2x^2 * y -13xy^2+10y^3 is divided by x-2y , then what is the remainder ?
Solution :
x-2) 3x^3 - 2x^2 * y -13xy^2+10y^3 ( 3x^2+4xy-5y^2
3x^3- 6x^2y
-----------------------------
4x^2y -13xy^2
4x^2y -8 xy^2
------------------------------------------
-5xy^2 +10y^3
-5xy^2+10y^3
-----------------------------------------------
Remainder = 0
Ques 6.
If 2600 is divided among 3 persons X,Y and Z in ratio 1/2 :1/3 : 1/4 , How much does Y gets ?
Solution :
==> 1/2 :1/3 : 1/4 = 6 :4:3
Y gets = 4/13 * 2600 = 800
Ques 7.
Two trains of lengths 100m and 150m are travelling in opposite directions at speeds 75 kmph and 50kmph respectively. What is the time taken by them to cross each other?
Solution :
Total length to cross each other = 100+150 = 250m
Relative speed = 75+50=125kmph
By multiplying with 10 you will get , how many meters its travelled in 36sec
1250m -------------36
250 m. ---------- ?
Time = 36/5 = 7.2sec
Ques 8.
A fruit seller buys Oranges at 4 for a rupee and sells them 5 for three rupees. What is his gain per cent ?
Solution :
1/4 ----------100%
3/5 ---------- ?
= 3/5 * 100*4 = 120%
Profit = 120-100=20%
Ques 9.
The value of ( 0.9*0.9*0.9+0.2*0.2*0.2*0.3*0.3*0.3-3*0.9*0.2*0.3) / (0.9*09+0.2*0.2+0.3*0.3-0.9*0.2-0.2*0.3-0.3*0.9 ) = ?
Solution :
Its in ( a^3+b^3+c^3-3abc)/(a^2+b^2+c^2-ab-bc-ca) form
==>a+b+c
So
== 0.9+0.2+0.3 = 1.4
Ques 10.
80 liters of milk and water content 10% of water . The water to be added to make the water content 30% in the new mixture is ?
Solution :
Water : milk = 10 : 90 = 1:9
In 80 liters water = 8
Milk = 72
==> (water + x )/milk = 30/70 = 3/7
==> (8+x)/72 = 3/7
==> 56+7x = 216
==> 7x = 160
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