- The average weight of five friends P,Q,R,S and T is (x+6) years, while the average weight of R and T is (x-6) kg. If the weight of another person U is also added, then the average weight of all of them is reduced by 5 kg. Find the value of x, if the average weight of P,Q,S and U is 94.5.
7060809050Option D

Total weight of friends P,Q,R,S and T

= 5*(x+6) kg.

Total weight of P,Q and S = 5*(x+6) – 2*(x-6) = 3(x+14) kg

Weight of U = (x+6-5)*6 – (x+6)*5 = (x-24) kg

Now, [3*(x+14) + (x-24)] = 94.5*4

=> x = 90 - The profit percentage earned on selling an article for Rs.2400 is twice the profit percentage earned on selling an article for Rs.1800. Find the profit percentage on selling the article for Rs.1600.
55.20%33.33%23.45%40.25%17.15%Option B

Let the CP of article be Rs.x.

2400 – x = 2*(1800 – x)

=>x = 1200

Required Profit % = (1600 – 1200)/1200*100 = 33.33% - A and B deposited same amount in scheme A and scheme B resp. B deposited the amount at 20% per annum. The difference between interests earned by them after 2 years will be 6% of the amount deposited by each of them. If scheme A and scheme B offer simple interest and compound interest resp. Find the rate at which A deposited the amount.
30%15%25%18%20%Option C

Let the amount deposited by each of them and the rate at which A deposited the amount be Rs. x and y% resp.

Total interest earned by A in 2 years = 2xy/100 = Rs.xy/50

Total interest earned by B in 2 years = x*{(1.2)^2 – 1} = Rs.11x/25

Now, xy/50 – 11x/25 = 6% of x

=>x{(y-22)/50} = 33x/50

=>y = 25

Rate = 25% - Some cubes, each of the same side have been kept in a cuboidal box of breadth and height of 11 m and 6 m resp. The total surface area of the cuboidal box is 676 m^2. If the total surface area of the cuboidal box is 676 m^2. If the total surface area of each cube is 15000 cm^2. Find the number of cubes kept in the box to occupy the whole space.
74408450950084487550Option D

Let the length of the cuboidal box be x m.

And side of each cube be a cm.

Now, 2*(x*11+11*6+x*6) = 676

=>x = 16

Volume of the cuboidal box = 16*11*6 = 1056 cm^3

And , 6a^2 = 15000

=>a^2 = 2500

=>a = 50

Volume of each cube = 50*50*50 = 125000 cm^3 = 0.125m^3

Number of cubes = 1056/0.125 = 8448 - A shopkeeper sold an article at a profit of 28% after allowing some discount percentage. The cost price of the article was Rs.338 more than the discount given by the shopkeeper. Find the discount percentage if the marked price was Rs.1600.
32%25%42%20%30%Option A

Let the SP and discount be Rs.x and d% resp.

CP of the article = x/1.28 = Rs.25x/32

SP of the article = (100-d)% of 1600 = Rs.(1600 – 16d)

1600 – 16d = x

=>x+16d = 1600 16d = 1600 – x

And, 25x/32 – 16d = 338

=>25x/32 – 1600 + x = 338

=>(25x + 32x)/32 = 1938

=>x = 1088

Discount% = (1600 – 1088)/1600*100 = 32% - A boatman rows some distance downstream and half of it upstream. A submarine moving at the speed of 6 km/hr. against the stream can cover 3 km in 1 hour. If the speed of boatman in still water is 15 km/hr. and the total time taken by the boatman to cover the whole distance is 3.5 hours, then find the downstream distance travelled by boat.
30 km28 km36 km44 km52 kmOption C

Let the speed of the stream be y km/hr.

Relative speed of submarine with respect to the stream speed = (6-y) km/hr.

(6-y)*1 = 3

=> y = 3 km/hr.

Downstream speed = 15+3 = 18 km/hr.

Upstream speed = 15 – 3 = 12 km/hr.

Now, x/18 + (x/2)/12 = 3.5

=>x = 36 km - A train covers certain distance running at the speed of 60 km/hr. without any halt. Had the train took 12 halts and the average time per halt was 4 minutes , the total time taken to cover the desired distance by the train would have been 5.25 hours,. Find the distance covered by the train.
222 km159 km320 km250 km267 kmOption E

Total time taken by the train in all the stops

= 12*4 = 48 minutes = 0.8 hours

Total running time without any halt = 5.25 – 0.8 = 4.45 hours

Dist. Covered by train = 60*4.45 = 267 km - A container contains mixture of petrol and diesel in the ratio of 4:7 resp. 110 litres of mixture is sold Rs.533/11 per litre and then 40 litres of petrol is mixed and then remaining whole mixture is sold at Rs.51 per litre. If cost price of per litre or petrol and diesel is Rs.40 and Rs.50 resp. then find the total profit percentage earned upon selling all the mixture.
30%25%15%10%20%Option D

Let the quantity of petrol and diesel in the container be 4x litres and 7x litres resp.

Total CP = (4x+40)*40 + 7x*50 = Rs.10(51x+160)

Total SP = 110*533/11 + (4x+7x+40-110)*51 = 561x+1760 = Rs.11(51x+160)

Profit = Rs.(51x+160)

Profit% = {(51x+160)/10(51x+160)}*100 = 10% - A bag contains 3 red, 5 white and 4 black balls. Some balls of blue colour are put into the bag such that the probability of drawing a black coloured ball from the bag is reduced by 2/15. Find the probability of drawing blue balls from the bag.
10/9314/9517/9011/9113/90Option B

Let the number of blue balls put into the bag be x.

4/12 – 4/(12+x) = 2/15

=>x = 8

Required Probability = 8C2/20C2 = 14/95 - There are 10 men and 8 women in a bus, and only 8 seats are there in the bus. In how many ways will at least 4 women and at least 2 men occupy a seat in the bus?
21212 ways20000 ways23250 ways22680 ways21253 waysOption D

Number of ways = 10C4*8C4 + 10C3*8C5 + 10C2*8C6

= 14700 + 6720 + 1260 = 22680 ways