Aptitude Questions and Answers
A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B's money was used ?
B received 2/3 of the profit
=> A : B = `1/3 : 2/3 = 1:2`
Let the total capital = x
Then A's capital = `x/4`
B's capital = `x – x/4 = (3x)/4`
Assume B's money was used for b months
Then A:B = `(x/4)**15 : ((3x)/4)**b = 1 : 2`
=> `15/4 : (3b)/4 = 1 : 2`
=> `15 : 3b = 1 : 2`
=> `5 : b = 1 : 2`
=> `5/b = 1/ 2`
=> `b = 5**2 = 10`
There are 10 items in a box, out of which 3 are defective. 2 items are taken one after the other. What is the probability that both of them are defective?
probability = `3C2/10C2 = ((3!) / (2! * 1!))/((10!) / (8! * 2!)) = 1/15`
`1/15 * 4/4 = 4/60`
A vendor sold the item at Rs. 500 with a profit margin of 25%. What is the cost price of the item?
We know,
`Profit % = ((Selli ng Price - Cost Price))/(Cost Price) * 100`
`=>25 = ((500-x))/(x)*100`
=> 125x = 50000
=> x = 400
A shopkeeper bought a box of 100 toffees for Rs. 200. His son ate 10 toffees (ofcourse, without paying!). At what S.P should each toffee be sold so shopkeeper makes an overall profit of 20%?
C.P for shopkeeper = Rs.200
Required Profit % = 20%
=> Required Total S.P = 1.2 * 200 = Rs. 240
Toffees Left = 100 - 10 = 90
S.P for Each Toffee = 240/90 = Rs. 2.67
A petrol pump owner mixes 1 litre of solvent in 9 litres of Petrol. The cost price of solvent is Rs. 10 per litre and that of petrol is Rs.70 per litre. The selling price of the mixture is Rs. 76.8 per litre. What is the profit percentage?
C.P. of 10 litres of Mixture = 10*1+70*9 = Rs.640
S.P. of 10 litres of Mixture = 76.8 * 10 = Rs. 768
Thus Profit % = `((768-640)/640)*100`
=> Profit % = 20%
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. The sum of the digits in N is :
N = H.C.F of (4655-1305), (6905-4655) and (6905-1305) = H.C.F of 3360, 2240 and 5600
N= 1120, hence sum of digits in N= (1+1+2+0)= 4
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres, and length of the second train = 17y metres.
`(27x+17y)/(x+y) = 23`
27x + 17y = 23x + 23y
4x = 6y
`x/y = 3/2`
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq. metre.
Area of the floor = (5.5 x 3.75) m2 = 20.625 m2.
Cost of paving = Rs. (800 x 20.625) = Rs.16500.
A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
Clearly, we have : length(l) = 9 ft.
and l+2b = 37 ft.
i.e., 9+2b = 37
2b = 37-9
2b = 28
So, the breadth(b) = 14 ft.
Area = (l x b) = (9 x 14) sq.ft. =126 sq.ft.
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area in m2 is
The difference between the length and breadth is = 23 m.
i.e., (l - b) = 23-------- eq.(1)
And perimeter = 206 m.
i.e., 2(l + b) = 206
l + b = 103---------eq.(2)
By solving eq.(1) and (2), we get length(l) = 63 and breadth(b) = 40.
So, Area = ( l x b ) = (63 x 40) m2 = 2520 m2.
