# Quant Boosters - Hemant Malhotra - Set 4

• Method1- Direct formula when u want to choose r numbers out of n numbers such that no two values are consecutive = 12-4+1C4=9c4

Method2-
A... A1 .... A2 ... A3... A4 ..... B
here A1,A2,A3 and A4 are 4 halting stations
now A1,A2,A3,A4 should not be consecutive
NOW let x1 be d number of stations before A1
so x1>=0 (( its possible that after A , next station is A1 )
A1 and A2 should not be consecutive so there must be atleast one stations
so let number of stations x2
so x2>=1
same for A2 and A3
x3>=1
same for A3 and A4
x4>=1
now station After A4 could be zero also
so x5>=0
total station=12
and 4 are halting and 8 are other stations
so x1+x2+x3+x4+x5=8
where x1>=0 letx1=a
x2>=1 so x2=1+b
x3=1+c
x4=1+d
x5=e
so a+b+c+d+e=5
so number of ways=5+5-1C5-1=9c4

• Q27) Find the number of ways of distributing 27 ladoos to Swetabh, Raman and Gaurav such that number of ladoos Swetab gets are more than the number of ladoos Raman gets which in turn is more than the number of ladoos Gaurav gets?

• method 1
let G=x then R=x+y+1 and S=x+y+z+2
so 3x+2y+z+3=27
so 3x+2y+z=24
now make cases and solve u will get ur ans

method 2
S+R+G=27
now ordered=29c2
now here find unordered
case when 2 same one different
=2S+G=27
so G=27-2S
so S will vary from 0 to 13 so 14 values but 1 value will be there when all same
so 2 same one different case will be 13
and when all same
3S=27 so 1 case
so 6 * a + 3 * 13 + 1=29C2

• Q28) If numbers 320ab and 298cd are divisible by 35 and 65 respectively then find the number of divisors of [398cd – 320ab + 2]^10 where 320ab is the largest possible number satisfying the given conditions

• 320ab mod 35
means div by 5 and div by 7
so b could be o or 5
0ab-32 mod 7=0
ab-4 mod 7=0
ab mod 7=4
when b=5 then a = 9
max value of ab=95
now same process and u will find cd=45
OA: 41261 ; numbers will be 32095 and 39845.

• Q29) A salesman sells two kinds of trousers: cotton and woollen. A pair of cotton trousers is sold at 30% profit and a pair of woollen trousers is sold at 50% profit. The salesman has calculated that if he sells 100% more woollen trousers than cotton trousers, his overall profit will be 45%. However he ends up selling 50% more cotton trousers than woollen trousers. What will be his overall profit?
a. 37.5%
b. 40%
c. 41%
d. 42.33%

• Let Cotton CP=a
Woolen CP=b
now let Cotton = x then Woolen=2x
So SP of cotton=1.3 * x * a
and Wollen =1.5 * 2x * b=3 * x * b
now overall profit =x*((1.3a+3b))-((ax+2x*b))/((ax+2bx))
((0.3a+b))/(a+2b))=45/100=9/20
6a+20b=9a+18b
so 3a=2b

now let woollen =2x then cotton=3x
so CP = 2x * a + 3x * b
and SP = 2x * 1.3a + 3x * b * 1.5
so profit=((2.6a+4.5b-2a-3b)/(2a+3b)
((0.6a+1.5b))/(2a+3b))
here 3a=2b
so 40% approx

• Q30) 3 men and 5 women together can finish a job in 3 days. Working on the same job 3 women take 5 days more than the time required by 2 men . What is the ratio of efficiency of a man to a woman ?

• let total work=60 unit
3 M + 5 W per day work=20 unit
let M work done in one day=a
then work work done=(20-3a)/5
2 M work done in one day=2a
and 3 work done in one day=((60-9a)/5
now 60/2a = ((60/((60-9a)/5 -5
so 30/a +5 = 300/(60-9a)
find a then ratio

• @hemant_malhotra
Hello sir,
To the reference of the above question, I have a doubt. It says he makes 20% profit secretly and claims to sell at the 10% loss.

Then,
If cost price is 100 , he makes a loss of 10 I.e. 90(S.P.) but here he SECRETLY makes a profit of 20%. So won't that be 90/1.2?

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