Aptitude test series Set 10

ANSWER: 40 km

Explanation:
x = 7 km/hr ; y = 3 km/hr
Ds = 10 km/hr ; Us = 4 km/hr
Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.
10*t = 4*(t + 6)
6t = 24 ; t = 4 hours
d = 10*4 = 40 km

ANSWER: 360

Explanation:
Here the mark obtained by the candidate is 120 and the candidate fails by 78 marks.
Therefore the passing marks is (120+78) = 198
Let the total marks be x,
55/100 * x = 198
Hence x = 360

ANSWER: 85995

Explanation:
The % change in population of city in two years time is 1.05*1.05 = 1.1025 = 10.25%
Therefore, after 2 years the population of the city will be 1.1025 * 78000 = 85995

ANSWER: 50%

Explanation:
Selling price of 12 pens = cost price of 18 pens
Therefore, the profit is 6 pens and cost price is 12 pens.
% profit = profit/cost price * 100
= 6/12 * 100
= 50%

ANSWER: 7450

Explanation:
Cost price = 2086/(0.14 + 0.14) = 2086/0.28
= Rs.7450

ANSWER: 15

Explanation:
The present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.
The difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.

ANSWER: 36, 35

Explanation:
My brother was born 6 years after my sister was born and 3 years before I was born. Age of father during my brother’s birth = (30 + 6) = 36 years.
Age of mother during my brother’s birth = (38 – 3) = 35 years.
Hence, during the birth of my brother, my father was 36 years old and my mother was 35 years old.

ANSWER: 125m

Explanation:
When X runs 48m, Y runs 42m.
Hence, when X runs 1000m, Y runs (1000 * 42) / 48 = 875m
X beats Y by 125m.

ANSWER: 336

Explanation:
There are in all 11 letters in the word ‘CORPORATION’. Since repetition is not allowed, there are 8 different letters that can be used to form 3-letter word.

Therefore, total number of words that can be formed = ⁸P₃ = (8*7*6)

= 336

ANSWER: 0.5

Explanation:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
E = {HTT, THT, TTH, TTT}
n(S) = 8
n(E) = 4
P(E) =n(E) / n(S) = 4/8 = 0.5

ANSWER: 60

Explanation:
When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.

ANSWER: 24

Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 44
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 132
9x + 18 = 3x + 138
6x = 120
x = 20
Therefore, the largest number is 24.

ANSWER: 21%

Explanation:
As selling price is Rs.1100 for 10 bags, each bag is sold at Rs.110.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 110 = Rs.210.
%profit = 210/1000 *100
= 21%

ANSWER: 272

Explanation:
Cost price = Selling price/(1 + profit percent)
= 340/(1 + 0.25) = 340/1.25
= Rs.272

ANSWER: 1

Explanation:
5² = 25, on division by 6, the remainder is 1.
5³ = 125, on division by 6, the remainder is 5.
5⁴ = 625, on division by 6, the remainder is 1.
5⁵ = 3125, on division by 6, the remainder is 5.
Hence, for 5 ^(2x) on division by 6, the remainder is 1, and for 5^(2x-1) on division by 6, the remainder is 5.
Therefore, for 5⁷⁰, on division by 6, the remainder is 1.

ANSWER: 1079

Explanation:
Number of digits used in 1 digit numbers = 1*9 = 9
Number of digits used in 2 digit numbers = 2*90 = 180
Number of digits used in 3 digit numbers = 3*900 = 2700
Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320
Hence, number of pages with 4 digit number = 320/4 = 80
Total number of pages = 1079

ANSWER: 27

Explanation:
Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x)
3*x + (70 – x)*(-1) = 38
4x = 38 + 70 = 108
x = 27

ANSWER: 48

Explanation:
If A invests amount C1 for T1 time and his share of profit is P1, and B invests amount C2 for T2 time and his share of profit is P2, then, C1 * T1 / C2 * T2 = P1/P2
If P is the Viru’s share of profit, then Jay gets (240 – P)
Therefore, 6000 * 12 / 3000 * 6 = (240 - P) / P = 72/ 18 = 4
4P = (240 – P)
5P = 240
P = 48

ANSWER: 16 : 2 : 9

Explanation:
Let the profit of X be P1, that of Y be P2 and of Z be P3.
P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45
= 16 : 2 : 9

ANSWER: 65.61 litres

Explanation:
As Ram replaces 10% of kerosene with water, the amount of kerosene left is 90%.
As the replacement is done four times,
After 1st replacement, kerosene left is : 0.9*100 = 90 litres
After 2nd replacement, kerosene left is : 0.9*90 = 81 litres
After 3rd replacement, kerosene left is : 0.9*81 = 72.9 litres
After 4th replacement, kerosene left is : 0.9*72.9 = 65.61 litres

ANSWER: 5.25

Explanation:
Let the amount of milk be x.
36x = 28(x + 1.5)
36x = 28x + 42
8x = 42
x = 5.25 litres

ANSWER: 0.78 minutes

Explanation:
Total distance = addition of length of the two trains = 140 + 120 = 260 metres
As the two trains are travelling in the same direction, their relative speed is:
v = | v1 – v2 | = | 40 – 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min
t = 260/ 1000*3
t = 0.78 minutes

ANSWER: 66 km/hr

Explanation:
The relative speed of A and B is 6 km/hr = 1.67 m/s
As the car passes A after 10s, the distance between A and B after 10s (i.e. at 11th second) is the distance covered by car in 1 second.
Therefore, at t = 11, d = 1.67 * 11
d = 18.33 m
v = d/t = 18.33/1 = 18.33m/s
v = 66 km/hr

ANSWER: 15 minutes

Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes

ANSWER: 15.54%

Explanation:
The resultant profit = 1.06 * 1.09 = 1.1554 = 15.54%
Alternatively, the resultant profit = [x + y + xy/100]
= 6 + 9 + (6*9)/100
= 15 + 0.54
= 15.54%