- 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, [𝑥× 5/14 −10]/[ 𝑥× 9/14 −18+2] = 1/2

⇒[ 5𝑥−140]/[ 9𝑥−224] = 1/2

⇒ 10x – 280 = 9x – 224

⇒ 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 × (25.8 + 3.9) – 5 × 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) – (x – y) = 6

⇒ 2y = 6

⇒ y = 3 km/hr

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

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

ATQ, 4x + x – 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, {𝑥 + 8}/{ 𝑦 + 6} = 5/6

6x + 48 = 5y + 30

6x – 5y = – 18 … (i)

x + 10 = y + 6

x – y = – 4 … (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 × 5/18 = 20 m/s

Let length of train be x m

ATQ, 524 + 𝑥 55 = 20 x = 1100 – 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 Man’s efficiency = 2w unit/day

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

8 men and 4 women start work for 3 days

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

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

Days required = 100𝑤/16𝑤 = 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 cm³?
9 cm7 cm8 cm6 cm5 cmOption B

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

Radius = 2𝑥/2 = 𝑥 cm

Volume of cylinder = 𝜋𝑟^2ℎ

Now, 𝜋𝑟 ^2ℎ = 3234

=>22/ 7 × 𝑥^2 × 3𝑥 = 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) – 20/100 × 𝑃 = 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 × 2x : 12 × x : 8 × y

ATQ, 24x = 8y

y = 3x

Required Percentage = (12 × 𝑥)/(8 × 3𝑥) × 100 = 50%

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