Quant Boosters by VP - Set 2
Soln: from line 2= > A = 9 + B
from line 1= > A=4(A-18 )= > 3A = 72 = > A = 24 so B = 15
A says I am 4 of your age when i am as old as you are now. What is B’s age right now?? 9 years less than A
when A is of that age as B is now... then B will be 18 years younger than A’s current age....
means B ‘s age that time will be (A-18 )
then according to que A = 4(A-18 )
Q14) 4 parties Congress,BJP,AAP and BSP contested for all seats in an election.Each seat was won by exactly one of the 4 parties. Congress lost on 29 seats, BJP lost on 12 seats, AAP lost on 20 seats and BSP lost on 26 seats.What was the total no of seats being contested in the election?
For each seat there is 1 win and 3 losses
so total no of losses = 87 means no of seats = 87/3 = 29
Q15) Contractor undertakes to dig 10km long canal in 180 days and employs 40 men. After 60 days they finished only 2.5km of canal. To complete the wirk on time, how much more men needs to be hired?
Work done = 2.5 left=7.5 (3 times)
time = 60 days left=120 days(2 times)
so to do 3 times work in 2 times time, need 3/2 times men
3*40/2 = 60 men
so 6-40=20 more men needs to be hired.
Q16) There are 3 runners Aman, Badal and Carol. Aman beats Badal by 20m amd Carol by 34m. Badal beats Carol by 21m. Find length of race.
While Badal travelled 20m, Carol travelled 34-21=13m
so speed ratio B:C=20:13
so B/C = 20/13 = (L-20)/(L-34)
Q17) I wanted to buy 2 dozen bananas but I am 30 Rupees short. So I bought 20 bananas and 2 rupees is left with me. Price of 1 banana?
24 bananas cost= > 30 more than what I have
20 bananas cost = > 2 less than what I have
So 4 bananas cost 30+2=32rupees
1 banana cost 8 rupees
Q18) 100 kg grapes contains 98% water. After few days, due to evaporation some water evaporates and it contains 94% of water. Find weight of grapes.
98% water means 2% mass=2kg mass
When water evaporates, water=94% so mass =6%
but mass is constant so 2 kg = 6%
Numerator(mass) is same but fraction increased 3 times. So denominator decreased 3 times
100/3 = 33.33 kg new weight of grapes.
Q19) If 8 coins are tossed, what is the probability that no two heads appear consecutively.
Use Fibonacci function
F(0) = 1
F(1) = 2
F(2) = 1 + 2 = 3
F(3) = 2 + 3 = 5
F(4) = 3 + 5 = 8
F(5) = 5 + 8 = 13
F(6) = 8 + 13 = 21
F(7) = 13 + 21 = 34
F(8) = 21 + 34 = 55
So 55/2^8 Ans
It's like 3 coins ho tab find f(3)
4 coins ho tab f(4)
N coins k liye f(n) that's generalisation
Example try for 3 coins
Or directly f(3)/2^8 = 5/8
Q20) There were x pigeons and y mynahs in a cage. One fine morning p of them escaped to freedom. If the bird keeper, knowing only that p = 7, was able to figure out without looking into the cage that at least one pigeon had escaped, then which of the following does not represent a possible (x,y) pair?
a) (10, 8)
b) (7, 2)
c) (25, 6)
d) (12, 4)
For the bird keeper to figure out that at least 1 pigeon had escaped, the number of mynahs has to be less than 7. In other words, y < 7. Hence, the pair (10,8) is not a valid one.
Q21) Anuj likes to jog in a park. While jogging he also calculates his speed and the number of steps taken by him. He observes that the steps taken by him per minute are 5 times his speed in km/hr. What is the distance he covers per step if he jogs at a uniform speed ?
let x km per hr be the speed
so 5x steps per min = 5x * 60 = 300x steps per hour
so 300x steps = x km
300x steps = 1000x m
1 step = 10/3 m ?
Q22) The probability of a car passing a certain intersection in a 20 minute windows is 0.9. What is the probability of a car passing the intersection in a 5 minute window? (Assuming a constant probability throughout)
Probability of a car passing in a 20 minute window = 1 – (probability of no car passing in a 20 minute window)
Probability of a car passing in a 20 minute window = 1 – (1 – probability of a car passing in a 5 minute window)^4
0.9 = 1 – (1 – x)^4
(1 – x)^4 = 0.1
1 - x = .1^.25
x = 1 - .1^.25
Q23) When three brands of juices are mixed in the ratio of 3 : 4 : 5 and 4 : 5 : 6, the cost price of the mixture of these two juices comes out to be Rs. 20 and Rs. 25 per litre respectively. Find the cost price of a litre of mixture of juices in which the three brands are mixed in the ratio of 6 : 7 : 8.