Aptitude - Profit and Loss - Discussion

14. 

A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:

[A].
5 15 % loss
17
[B].
5 15 % gain
17
[C].
6 2 % gain
3
[D]. None of these

Answer: Option B

Explanation:

C.P. of 1st transistor = Rs. 100 x 840 = Rs. 700.
120

C.P. of 2nd transistor = Rs. 100 x 960 = Rs. 1000
96

So, total C.P. = Rs. (700 + 1000) = Rs. 1700.

Total S.P. = Rs. (840 + 960) = Rs. 1800.

Gain % = 100 x 100 % = 5 15 %
1700 17


Aastha said: (Mar 7, 2011)  
How did this 120 come ?

Kiran said: (Mar 16, 2011)  
Gain % i.e, 100+20=120

Mrs Pallavi said: (May 19, 2011)  
In simple way by using our logic,

sp1=840
p1=20%

sp2=960
p2=4%

cp1=(sp1*100)/(100+20).....by formula of profit
cp1=(840*100)/(100+20)
cp1=700

here gain is 840-700=140

cp2=(sp2*100)/(100-4).....by formula of loss
cp2=(960*100)/(100-4)
cp2=1000

loss is 1000-960=40

therefore total gain=140-40=100

profit%=(actual profit /cp)*100
=100/1700*100
=100/17
=5.88%

ans (b)

Kiran Sharma said: (Jun 18, 2011)  
Very Easy

Apply formula of Cost price in both cases of profit and loss
c.p. = 100*sp/100-gain% and also of Cp = 100*sp/100-loss%
and in this way you will get cost price of both cases
and then add both cost prices to get total cost price

afterwards also add both selling price to get total s.p.

and then subtract it to get profit

apply profit % formula to get profit amount

Priya said: (Jan 28, 2012)  
How gain 100 came?

Mounika said: (Jun 8, 2012)  
Thanks for your explanation pallavi. Its useful.

Bhavna said: (Jun 30, 2012)  
How gain 100 came in last step ?

Varsha said: (Aug 18, 2012)  
Total sp is (840+960)=1800
cp=1700
gain=(sp-cp)=1800-1700=100
so gain%=(100/1700*100)

Suresh said: (Aug 7, 2013)  
@Priya.

Gain = (S.P-C.P/C.P*100).

= (1800-1700/1700*100).

= (100/1700*100).

= (100/17).

Madhav Kakkar said: (Jul 26, 2014)  
Does anybody know another shortcut it's time consuming method?

Haritha said: (Dec 22, 2014)  
Can any one tell me why we used 100/120 instead of 120/100?

Preet said: (Apr 11, 2015)  
Please give a shortcut of this question.

Gargi Das said: (Jun 8, 2015)  
This is nothing but cross multiplication @Haritha, see:

In 100 Rs gain is 120.

In 840 Rs gain is 120*840/100.

This process is same for loss also.

Kiruthi said: (Jun 20, 2015)  
120% C.P 1 = S.P 1 = Rs. 840 (120% = 100% + 20% profit).

C.P 1 = 840*100/120 = Rs. 700 (120% = 120/100).

96% C.P 2 = S.P 2 =Rs. 960 (96% = 100% - 4% loss).

C.P 2 = 960*100/96 = Rs. 1000 (96% = 96/100).

Total C.P = 700+1000 = 1700.

Total S.P = 840+960 = 1800.

Total profit = Total S.P-Total C.P = 1800-1700 = 100.

Gain % = (Profit/C.P)*100 = (100/1700)*100 = 100/17 = Answer.

Kiruhti said: (Jun 20, 2015)  
120%C.P1 = S.P1 = 840 (120% = 100% + 20% profit).

C.P1 = 840*100/120 = 700 (120% = 120/100).

96% C.P2 = S.P2 = 960(96% = 100% - 4% loss).

C.P2 = 960*100/96 = 1000(96% = 96/100).

Total C.P = 700+1000 = 1700.

Total S.P = 840+960 = 1800.

Total profit = 1800-1700 = 100.

% Gain = (Total profit/Total C.P)*100.

= (100/1700)*100 = 100/17 = Answer B.

Saba said: (Sep 19, 2015)  
Can some one tell me, why not these?

S.P 1 = 840.

Gain of 20% of 840 = 20/100*840 = 168.

Then C.P1 = S.P-Gain.

= 840-168 = 672.

Saba said: (Sep 19, 2015)  
S.P1 = 840.

Gain of 20% = 20/100*840 = 168.

Since C.P = S.P - Gain.

C.P1 = 840-168 = 672.

So why above C.P 700?

E.g: If S.P = 10.

Gain% = 50%.

C.P ?

Then gain = 50% of 10 = 50/100*10 = 5. For C.P, since C.P = S.P - Gain.

= 10 - 5.

C. P = 5.

Saba said: (Sep 19, 2015)  
I have problem in C.P, please guide me.

S.P1 = 840.

Gain = 20/100*840 = 168.

C.P1 = 840 -168 = 672.

Now S.P2 = 960.

Loss = 4/100*960 = 38.4.

C.P2 = Loss+S.P.

= 38.4+960 = 998.4.

Total C.P = 998.4+672 = 1670.4.

Total S.P = 1800.

Sainik said: (Nov 4, 2015)  
Remember if C.P is 100 then S.P is 120 (If 20% gain, if 4% loss then C.P is 100 S.P is 96).

Meenu said: (Nov 27, 2015)  
Please explain it in shortest and easy way.

Balu said: (Jan 23, 2016)  
Cp of trans1 = 100*840/120 = 700.

Cp of trans2 = 100*960/96 = 1000.

Gain = 400*100/1700 = 400/17.

Felix said: (Oct 15, 2016)  
@Priya,

Let we assume 100 if the base cost price is not given.

Dinesh said: (Nov 20, 2016)  
Can we solve this using alligation?

Meena said: (Nov 26, 2016)  
I am confused please solve this in a simple and clear way.

Satya said: (Mar 18, 2017)  
Let cost price = x;
Case1:sp=840,profit=20%
x=840-0.2x;
1.2x=840;
x=700.

case2: sp= 960,loss=4%
x=960+0.04x;
0.96x=960;
x=1000.

Total cp=700+1000=1700; Total sp=840+960=1800;
1800-1700 = 100(Gain)
Gain% = (100/1700) * 100 gives the answer.

Satish said: (May 19, 2017)  
How can 5.88 can be converted to 5 * 15/17?

Cathy said: (Sep 7, 2017)  
How can we say here loss is incurred?

Shinjinee Ghatak said: (Oct 6, 2017)  
What is the gain% formula? Please tell me.

Surya said: (Dec 15, 2017)  
c.p. = s.p/profict%+c.p.%

Easy method find cost price.
C.P. % = 100 %.
So, 840/100+20 = 840/120 = 700.

Sanjay said: (Jun 26, 2018)  
@Satish.

It is 100/17 so 17*5=85 and reminder is 5 and balance is 15.

Faklandu said: (Aug 1, 2018)  
Why not A? Here it is asking both gain or loss right?

Rakesh said: (Aug 22, 2018)  
How CP can be calculated easily? Can anyone give me the shortcut?

Rohit said: (Sep 24, 2018)  
Very good explanations. Thanks all.

Sandeep said: (Feb 6, 2019)  
At last in the gain formula, how can we take gain as 100? please can someone explain.

Sidharth Singhaniya said: (Feb 7, 2019)  
Can Anyone solve it by Easy Ratio Method ?

Ameer said: (Mar 17, 2019)  
S.P of 1 translator = 840.
S.P of another translator = 960,
we have to find loss or gain?

Formula is;
c.p={100/(100+gain%)} * s.p,
c.p=100/(100+20%) * 840,
So c.p= 700.

which means gain=840-700 = 140,
Now to second translator;
c.p={100/(100-4%)} * 960,
c.p=1000.

Which means loss=1000-960 = 40,
Now we observed that the total cost price is 1000+700 = 1700,
Total gain = 140-40 = 100.
Gain % = 100 x 100/1700= 5.88%.

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