- In a vessel, there are two types of liquids A and B in the ratio of 5 : 9. 28 lit of the mixture is taken out and 2 lit of type B liquid is poured into it, the new ratio(A:B) thus formed is 1 : 2. Find the initial quantity of mixture in the vessel?
48 L67 L62 L56 L50 LOption D

Let the initial quantity of mixture in vessel be x l

ATQ, [π₯Γ 5/14 β10]/[ π₯Γ 9/14 β18+2] = 1/2

β[ 5π₯β140]/[ 9π₯β224] = 1/2

β 10x β 280 = 9x β 224

β x = 56 L - The average weight of 5 students in a class is 25.8 kg. When a new student joined them, the average weight is increased by 3.9 kg. Then find the approximate weight of the new student.
38 kg32 kg49 kg40 kg43 kgOption C

Weight of new student = 6 Γ (25.8 + 3.9) β 5 Γ 25.8 = 49 kg - The difference between downstream speed and upstream speed of boat is 6 km/hr and boat travels 72 km from P to Q (downstream) in 4 hours. Then find the speed of boat in still water?
14 km/hr.15 km/hr.11 km/hr.12 km/hr.10 km/hr.Option B

Let the speed of boat in still water be x km/hr and that of stream be y km/hr

ATQ, (x + y) β (x β y) = 6

β 2y = 6

β y = 3 km/hr

Downstream stream = (x + y) = 72/4 = 18 km/hr

β x = 15 km/hr. - The sum of four times of an amount βxβ and (x β 9.75) is Rs. 442. Find the approximate value of x.
Rs. 50Rs. 60Rs. 90Rs. 80Rs. 70Option C

ATQ, 4x + x β 9.75 = 442

5x = 451.75

x = Rs. 90 - The ratio of age of Ishu 8 years hence and that of Ahana 6 years hence is 5 : 6. The age of Ishu 10 years hence is equal to the age of Ahana 6 years hence. Then, find the present age of Ishu.
6 years5 years2 years3 years4 yearsOption C

Let present age of Ishu & Ahana be x year & y year respectively

ATQ, {π₯ + 8}/{ π¦ + 6} = 5/6

6x + 48 = 5y + 30

6x β 5y = β 18 β¦ (i)

x + 10 = y + 6

x β y = β 4 β¦ (ii)

x = 2 years

Present age of Ishu is 2 years. - A train of some length passes the platform of length 524 m in 55 seconds. Find the length of train if the speed of train is 72 km/hr.
515 m520 m525 m576 m500 mOption D

Speed of train in m/s. = 72 Γ 5/18 = 20 m/s

Let length of train be x m

ATQ, 524 + π₯ 55 = 20 x = 1100 β 524 = 576 m - 7 men and 6 women together can complete a piece of work in 8 days and work done by a women in one day is half the work done by a man in one day. If 8 men and 4 women started working and after 3 days 4 men left the work and 4 new women joined then, in how many more days will the work be completed.
6.25 days3.18 days6.20 days5.14 days4.12 daysOption A

Let efficiency of one women = w unit/day Manβs efficiency = 2w unit/day

Total work = (7 Γ 2w + 6 Γ w) Γ 8 =160w unit

8 men and 4 women start work for 3 days

Total work done = (8 Γ 2w + 4 Γ w) Γ 3 = 60w

4 women replace 4 man = (4 Γ 2w + 8 Γ w) =16w

Days required = 100π€/16π€ = 6.25 days - The ratio of the diameter of base and height of a cylinder is 2 : 3. Find the radius of the cylinder if the approximate volume of cylinder is 3234.01 cmΒ³?
9 cm7 cm8 cm6 cm5 cmOption B

Let diameter of base be 2x cm & height of cylinder be 3x cm

Radius = 2π₯/2 = π₯ cm

Volume of cylinder = ππ^2β

Now, ππ ^2β = 3234

=>22/ 7 Γ π₯^2 Γ 3π₯ = 3234

=> x = 7 cm = radius - What is the difference between 20% of P and 20% of (P + 5000).
10001400130015001200Option A

Required difference = 20/100 (P + 5000) β 20/100 Γ π = 1000 - A and B entered into a partnership by investing some amounts. The investment of A is twice of the investment of B. Another person C joined them after 4 months. At the end of a year, the profit share of A and C is equal. Then find the profit share of B is what percent of the profit share of C.
50%10%20%30%40%Option A

Let the Investment of B be Rs. X

Investment of A = Rs 2x

Ratio of profit, A : B : C

12 Γ 2x : 12 Γ x : 8 Γ y

ATQ, 24x = 8y

y = 3x

Required Percentage = (12 Γ π₯)/(8 Γ 3π₯) Γ 100 = 50%