Quant Boosters  Swetabh Kumar  Set 4

one man in 20 * 20=400 days so 1/400 in 1 day
so X * 20 * 1/400 + 30 * (15x)/400 = 1
20X + 450  30x = 400
so X = 5

Q26) One Indian, one Chinese and one Japanese worked for a company for the same period. The Indian is twice as efficient as Chinese and the Chinese is thrice as efficient as a Japanese. If Rs. 10,00,000 were given to all the three together, then calculate the amount received by the Chinese and the Japanese together.

OA: 4 lakhs.
Concept: Amount is divided in ratio of total work done by person / total work done in aggregate
so Japanese: Chinese: Indian = 1:3:6 so reqd: (1+3)/10 * total

Q27) Amit takes 20 days to complete a certain work. Amit started the work and Suraj joined him 4 days before the work was completed. Find out the number of days for which Amit worked alone if Suraj’s efficiency is 25% more than that of Amit’s.

Amit : 20 days
Suraj: 4/5 * 20 = 16 days
so N/20 + 4 * (1/20+1/16) = 1
N/20 + 4 * 9/80 = 1
4N+36=80 so N=11 days

Q28) A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half of the remainder heard one third of the talk and the other half heard two thirds of the talk. What was the average number of minutes of the talk heard by members of the audience?

(20 * 60 + 10 * 0 + 35 * 20 + 35 * 40)/100 = 33 minutes

Q29) A regular octagon with sides 1 unit long is circumscribed in a circle . Find the radius of the circle.

Center angle = 360/8 = 45.
cos 45= 1/rt 2 = 2r^21 /2r^2
rt 2 r^2 = 2r^21
r = sqrt {1/ (2rt2)}
= sqrt { (2+ rt2)/2 }

Q30) Find number of interval values of a for which roots of x^2 + ax + a = 0 are rational

a^2  4a = k^2
(a2)^2  k^2 = 4
(a  2  k)(a  2 + k) = 2 * 2, 2 * 2
2a  4 = 4 or 4
a = 4 or a = 0