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Ratio and Proportion
In what ratio must a person mix 3 kinds of tea costing rs 60/kg, 75/kg, 100/kg so that the resultant mixture when sold at 96/kg yields a profit of 20 %
ans is 1:4:2
is there any cross method short cut for such kind of problem??? pls help
Read Solution (Total 5)
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- The resultant mixture is sold at a profit of 20% at Rs.96/kg
i.e. 1.2 (cost) = Rs.96 => Cost = = Rs.80 / kg.
The best way to solve a problem of this kind is to go from the answer choices
The resultant ratio QA : QB : QC :: 1 : 4 : 2.
1 kg of variety A at Rs.60 is mixed with 4 kgs of variety B at Rs.75 and 2 kgs of variety C at Rs.100.
The total cost for the 7 kgs = 60 + (4 * 75) + (2 * 100) = 60 +300 + 200 = 560.
Cost per kg of the mixture = 560/7 = 80 kgs - 10 years agoHelpfull: Yes(24) No(13)
- 96/kg yields a profit of 20%
take an example selling price=100%+profit 20%
100/120=5/6
5*96/6=480/6=80
cost=80rs/kg
apply option to we can get esly ans...
1:4:2
(60*1)+(75*4)+(100*2)=60+300+200=560
560/(1+4+2)=80
80==80 Ans !!!!...
- 10 years agoHelpfull: Yes(18) No(0)
- this problem can only be solved by using hit and trial using the options
given,
s=96 rs/kg
profit= 20%
i.e. 20% of cost price
p= 20/100 * cp
p= cp/5
wkt,
s=p+c
96=c/5 +c= 6/5 c
c= (96*5)/6= 80rs/kg
CONSIDERING PRICE--->
we can write,
k(60k +75y +100z)=80 ...(B)
CONSIDERING WEIGHT-->
for 1 kg of required mixture,
k(x+y+z)=1 [taking k as proportionality consatnt]
k=1/(x+y+z)..(A)
now, if we substitute the option 1:4:2,
using (A),
k=1/(1+4+2)
k=1/7
and now using (B),
1/7(60+300+200)=80
1/7 * 560=80
80 =80
hence, our assumpstion for the option 1:4:2 is correct
- 10 years agoHelpfull: Yes(7) No(0)
- go through options
for ex:-1:4;2 than cost is =1*60+4*75+2*100=560
than 560*120/100=720
which satisfy the question - 10 years agoHelpfull: Yes(1) No(0)
- The resultant mixture is sold at a profit of 20% at Rs.96/kg
i.e. 1.2 (cost) = Rs.96 ⇒ Cost =96/1.2=Rs.80 / kg.
Let the three varieties be A, B, and C costing Rs.60, Rs.75 and Rs.100 respectively.
The mean price falls between B and C.
Hence the following method should be used to find the ratio in which they should be mixed.
Step 1:
Find out the ratio of Qa:Qc
using alligation rule:
Qa/Qc=(100−80)/(80−60)=1/1
Step 2:
Find out the ratio of Qb:Qc
using alligation rule:
Qb/Qc=(100−80)/(80−75)=4/1
Step 3:
Qc, the resultant ratio of variety c
can be found by adding the value of Qc in step 1 and step 2=1+1=2
The resultant ratio Qa:Qb:Qc::1:4:2
- 8 years agoHelpfull: Yes(0) No(0)
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