# Quant Boosters - Hemant Malhotra - Set 6

• Method1- c.p.100
m.p.125
sp..125 * 7/8==109.375
so profit==9.37%

Method2- let CP=1
MP=1+1/4=5/4
and 12.5%=1/8 discount
so 5/4 * 7/8=35/32
so profit=35/32-1=3/32 * 100=9.37%

• Q5) A car leaves P at 8 AM and travels to Q at a constant speed. A bus leaves Q at 8:45 AM and travels to P at a speed three times that of the car. If they meet at 10:00 AM, find the ratio of the distance traveled by the bus to the distance traveled by the car when they meet.

• S = speed of car
D1 = distance of car
D2 = distance bus
D1=2s
D2=(2-3/4)(3s)
D2=15/4s
D1:D2
2s:15/4s
Ratio is 8:15

• Q6) A, B and C start simultaneously from X to Y. A reaches Y, turns back and meet B at a distance of 11 km from Y. B reached Y, turns back and meet C at a distance of 9 km from Y. If the ratio of the speeds of A and C is 3:2, what is the distance between X and Y

• Let a, b, c are the speeds of A, B, C respectively;
let x be the distance between X and Y. Note that speed is proportional to distance.
We have
a/b = (x+11)/(x-11) and b/c = (x+9)/(x-9) and a/c = 3/2,
(x+11)/(x-11) * (x+9)/(x-9) = (a/b)(b/c) = a/c = 3/2,
2(x^2+20x+99) = 3(x^2-20x+99),
x^2-100x+99 = 0,
(x-1)(x-99) = 0.
bcz x > 11, so x = 99 km.

• Q7) A beaker contained V litres of a mixture of milk and water, with milk and water in the ratio of 3 : 2. The total volume of the mixture was increased by 60% by adding water. Next, 38.4 litres of the solution in the beaker was replaced by water. If the final ratio of milk and water in the beaker is 3:7, then find the value of V (in litres)
a) 80
b) 96
c) 120
d) 192

• Milk=3v/5
and water=2v/5 +(v * 60/100)=2v/5+3v/5=v
now 38.4 liter removed
so MF=(8v/5 -38.4)/(8v/5)
so milk=3v/5 * (8v/5 -38.4)/(8v/5)'
now equate to ratio and answer = 192 x 5/8 = 120

• Q8) In how many ways can 6 letters A, B, C, D, E and F be arranged in a row such that D is always somewhere between A and B?
a) 324
b) 240
c) 60
d) 48

• ways to arrange D,A,B =3! but we need A,D,B or B,A ,D so out of 3! , 2 favorable cases , so out of 6! we have 2/3! * 6! = 6 * 5 * 4 * 2 = 240

• Q9) Raju has forgotten his six-digit id number, he remembers the following: the first two digits are either 1,5 or 2,6,the number is even and 6 appears twice. If Raju uses a trial and error process to find his ID number at the most, how many trial does he need to succeed?

• when 1,5 at first two place
then last four places a b c d
when d=6 then out of 3 places one place will be filled by 6 so 3c1 and rest two have 9 choices so
3c1 * 9 * 9 = 243
now when d=0/2/4/8 so 4 choices so out of 3 places 2 places will be filled by 6 and one place have 9 choices so 3c2 * 9 * 4 = 108
now when 2,6 at first two places then d=6 then other 3 places have 9 * 9 * 9 = 729 choices
and when d=0/2/4/8 then one place should have 6 and rest 2 places have 9 choices so 4 * 3c1 * 9 * 9 = 972
so sum=2052

• Q10) If average of 20 double digit numbers is 18 , but becomes 21.8 when we interchange digits of a no , then how many original no's are possible ?

• (10a1+b1+10a2+b2+....10a20+b20)=360
10(a1+a2+a3+...a20)+(b1+b2+...b20)=360
now
10*(b1+b2+b3+...b20)+(a1+a2+a3...a20)= 436.0
so 9(b1+b2+...b20)-9(a1+a2+....a20)=76
so this is factor of 9 so not possible case

• Q11) Find numerically the largest term in the expansion of (2+3x)^9 when x=3/2

• (n-r+1)/(r) * (a/x) >= 1
(10-r)/r * (3x/2) >= 1
(10-r)/r * (9/4)>= 1
90-9r > = 4r
so 13r < = 90
r < = 6.9
so r = 6
so 7th term

• Q12) If a quadrilateral with sides 2, 3, 4 and 5 is inscribed in a circle and circumscribed to another circle then
find area of Quadrilateral

• Direct formula : If any quadrilateral with sides a, b, c and d inscribed in a circle and circumscribed to another circle then area of quadrilateral is sqrt(abcd). So here answer is sqrt(120)

• Q13) Find remainder when 1^99 + 2^99 + 3^99 + .... + 99^99 is divided by 100

• 1 to 99 there are 99 terms
1^99+99^99 will be div by 100
2^99+98^99 will be div by 100
now 49^99+51^99 mod 100=0
but there will be one more term
50^99 mod 100
which is also divisible by 100
so OA=0

• Q14) How many integral solutions (a,b) does the equation a^b=a * b have
a) 1
b) 2
c) 3
d) 4
e) More than four

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