Latest CAT Aptitude Question SOLUTION: Instead of a meter scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 percent on cash pay

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Instead of a meter scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 percent on cash payment, what is his overall percent profit?

Asked In CAT Devendra Marghade (11 years ago)

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chaitanya  (11 years ago)

let the price of 100cm cloth be Rs100 but now he get 120cm cloth for 100 rupees.

actual cost of 1cm =100/120
=5/6
now instead of selling 100cm by cheating he sells 80cm cloth for 100 rupees

now the profit is ......?

C.P of 80cm cloth is (5/6)x 80= Rs 66.66

S.P of 80cm cloth is at a discount of 20%is 100x0.8= Rs 80

now %profit = [(80-66.66)/66.66]x100
= 20.01%

so theprofit is approximately 20%

Is this solution Helpfull? Yes (8) | No (4)  

Vignesh  (11 years ago)

Overall profit % = 20.01%

Let the price of 100cm cloth = 100
But, he gets 120cm of cloth for 100rs.
Hence,

Actual Cost per cm = 100/120 = Rs.5/6

He sells 80cm of cloth instead of 100cm in the cost price of 100cm of cloth.

So, profit of 80cm of cloth = 5/6*80 = Rs.66.66

Selling price of 80cm of cloth at a discount 20% = 100 *0.8 = Rs.80

Therefore,

Profit percentage = (80-66.66/66.66)*100 = 20.01%

Is this solution Helpfull? Yes (3) | No (3)  

OMKAR GANDHI  (6 years ago)

Assume the merchant purchases 1 meter (100 cm) cloth at Rs.100.

Since he users 120 cm scale, he actually gets 120 cm of cloth.
=> Cost price of 120 cm cloth = Rs.100
=> Cost price of 100 cm cloth =
(100×100)/120
=1000/12
(100×100)/120=1000/12

Assume the merchant sells 100 cm cloth.
=> Selling price of 100 cm cloth = Rs.80 (∵ discount of 20%)

Since he uses 80 cm scale, he actually sells only 80 cm cloth and the cost mentioned above is the selling cost of 80 cm cloth.
i.e., Selling price of 80 cm cloth = Rs.80
=> Selling price of 100 cm cloth =
(80×100)/80=(100/80)×(100/80)=100

Profit = ((100−1000/12)×100)/1000/12
(100−1000/12)×100)1000/12
=((200/12)×100)/1000/12=200×100/1000=20%

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kln  (5 years ago)

a piece of cloth 100cm =100rs
by using 120cm scale instead of 100
actual =100/120=5/6
he selling 80 cm=>80/100=4/5
there fore=5/6*4/5=>4/6
he offer 20% discount=80rs
profit%=(80-66.66/66.66)*100

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