M4maths Previous Puzzles

29 Jan 2016 Mixture

A shopkeeper buys two kinds of tea, the price of the first kind being twice that of the second. He sells the mixture at Rs.17.50 per kg, thereby making a profit of 25%. If the ratio of first and second kinds of tea in the mixture be 2:3, find the cost price of each kind of tea.

OPtion

1) Rs.30 per kg and Rs.15 per kg
2) Rs.20 per kg and Rs.20 per kg
3) Rs.25 per kg and Rs.45 per kg
4) Rs.40 per kg and Rs.15 per kg
5) Rs.60 per kg and Rs.30 per kg
6) Rs.28 per kg and Rs.14 per kg
7) Rs.50 per kg and Rs.25 per kg
8) Rs.44 per kg and Rs.22 per kg
9) Rs.20 per kg and Rs.10 per kg
10)Rs.40 per kg and Rs.20 per kg

Solution

In 1 kg of mixture
tea of 1st kind = 2/5 kg
and tea of 2nd kind = 3/5 kg
Le the price of first kind of tea be Rs.x per kg.
Then, price of second kind = Rs.(x/2) per kg
Therefore Price of 1 kg mix = Rs.(2x/5 + 3x/10) = Rs.(7x/10)
But C.P. of mix per kg = Rs.(17.50*100 / 125) = Rs.14
Therefore 7x/10=14
then find x

Option 9) Rs.20 per kg and Rs.10 per kg

Correct Option: 9 Best Solution (15)

SHUBHAM   8 years AGO

using the method of alligations.
let price of first item be 2*X and price of second item b X.also the mixture is sold at the rate of 17.5 per kg with a profit of 25%.
thus price per kg would be Rs 14.
now framing the equations,
(x-14)/(14-2*X)=(2/3).
solving for X we get, X=10,hence the prices are 20,10
option...(9).

Like? Yes (17) | No (4)  

Prakash Panda   8 years AGO

125%=17.5
100%=14

now we know the ratio is 2:3 i.e
40%:60%

now check the option which gives u the xact 14 with the sum of 40 n 60% of 2 kind of tea.

40% of 20 is 8
60% of 10 is 6

Like? Yes (3) | No (1)  

Devendra Marghade   8 years AGO

If CP of 1st kind of tea=2x & 2nd kind of tea=x,
As on selling at Rs. 17.5 per kg. he gets profit of 25%, so his CP/kg must be 17.5*100/125=14 Rs.
If he takes 2y & 3y of these two kinds of tea respectively, then [(2x*2y)+(x*3y)]/((2y+3y)= 14 or 7xy/5y=14, x=10, So 2x=20
Option 9)

Like? Yes (2) | No (1)  

Gaurab Kumar Jha   8 years AGO

cp= (100/125)*17.50 =14
and by checking it on options we will find option 9 will be correct

Like? Yes (3) | No (2)  

Ram Kumar Prajapati   8 years AGO

Let Tea1 has cp= 2x and Tea2=x
cp of mixture= 17.5/125% = 14
Using allegation:
(14-x)/(2x-14)= 2/3
we get 2x=20 and x=10

Like? Yes (1) | No (1)  

Ravi P   8 years AGO

given 125%=17.5->100%=14
let first kinb be "x" and seconb be "Y"
given ratio x:y=2:3
so total 2+3=5 parts
-> (x*2/5)+)y*3/5)=15
we know x=2y;
->4y/5+3y/5=14;
y=14*5/7
y=10;
so x=20;
option 9

Like? Yes (1) | No (1)  

Richa Jain   8 years AGO

S.P of mixture=Rs 17.50/kg
P=25%
So, C.P of mixture= Rs 14/kg
T1/T2= (T2-14)/(14-2T2)
2/3= (T2-14)/(14-2T2)
T2= Rs 10/kg
T1=2T2= Rs 20/kg

Like? Yes (1) | No (1)  

suryakant singh   8 years AGO

selling price on the profit of 25% =17.50
cost price of mixture =14
then if price of second type = x
then frst type =2x
(x-14)/(14-2x)=2/3
hence,x=10 then 2x=20
answer is 20 and 10

Like? Yes (1) | No (1)  

Nazmul Hasan   8 years AGO

S.P. @ 17.50 with 25% profit, i.e, CP=14.
now, .4*2x+.6*x=14
thus, a=10.
so CP of 1st & 2nd kind will be 20 & 10.

Like? Yes (2) | No (2)  

harsh dhir   8 years AGO

let the tea be in ratio=2x and 3x
total quantity=5 x
S.P. of one kg=Rs.17.50
Total S.P.=17.50*5=Rs.87.50
Profit=25 %
C.P.=87.50/125 *100=Rs.70
Since the cp of 1st kind of tea is twice the second,
4x+3x=70
x=10
Therefore CP of 1st tea=Rs.20
Cp of 2nd Tea=Rs.10

Like? Yes (1) | No (1)  

GOURANGA SUNDAR MANDAL   8 years AGO

lex he buys 2x kg first kind tea and 3x kg second kind of tea.
And the price of the first kind of tea is 2y RS.per kg and second kind is y RS. per kg.
so the total cost =(2x*2y +3x*y)
making cost of per kg is=(2x*2y +3x*y)/(2x+3x)
according to qus {(2x*2y +3x*y)/(2x+3x)} *125/100=17.50
calculating this equ ..we get y 10, and 2y=20...
so option 9 is correct answer

Like? Yes (1) | No (1)  

pramit   8 years AGO

let prices of A and B be 2x and x
weights be 2/5 kgs and 3/5 kgs
cp=2/5*2x+3/5*x=7x/5
profit=25%0f 7x/5
sp=17.50
7x/5+25%of7x/5=17.50
x=10
2x=20

Like? Yes (1) | No (1)  

sachin sawant   8 years AGO

SP=17.50
SP=(1+25/100)*CP
17.50=125/100*CP
CP of mixture=14
let CP of first tea be 2x&CP of second tea be x
Hence CP of mixture=2x*2+x*3/2+3
Hence 14=7x/5
x=10& 2x=20
CP of first tea=20
CP= of second tea=10

Like? Yes (1) | No (1)  

Rajani P C   8 years AGO

125% --- 17.50
100%----14
2x x
/
14
/
x-14. 14-2x

x-14. 2
------ = --- then x=10 and 2x=20
14-2x 3

Like? Yes (1) | No (1)  

Abhineet kumar   8 years AGO

let the price of second kind tea is x
so cost price of first kind is 2x
sell price is 17.50 at 25% profit
so cost price is (100/125)*17.50=14
from the rule of alligation and mixture
(2x-14/14-x)=2/3
x=10
and is 20,10

Like? Yes (4) | No (5)