DIFFICULT PROBLEMS
1.The of an article including the sales tax is Rs 616.The rate of sales tax is 10%,if the shopkeeper has made a profit of 12%,then the cost price of the article is?
Sol: 110% of S.P=616
S.P=(616*100)/110=Rs 560
C.P=(100*S.P)/(100+gain%)
C.P. =(100*560)/(100+12)=Rs 500
2.Sam purchased 20 dozens of toys at the rate of 375 Rs per dozen .He sold each one of then at the rate of Rs 33.What was his percentage profit?
Sol: C.P of one toy=Rs 375/12=Rs 31.25
S.P of one toy=Rs 33
profit=S.P-C.P=33-31.25=Rs 1.75
profit %=(profit/C.P)*100
=(1.75/31.25)*100
profit% =5.6%
3.Two third of consignment was sold at a profit of 5% and the remainder at a loss of 2%.If the total was Rs 400,the value of the consignment was?
Sol: let the total value be Rs x
value of 2/3=2x/3, value of 1/3=x/3
total S.P value be Rs x
total S.P=[(105% of 2x/3)+(98% of x/3)]
=(105*2x)/(100*3)+(98/100)+x/3
=308x/300
(308x/300)-x=400
8x/300=400
x=(300*400)/8=Rs 15000
4.Kunal bought a suitcase with 15% discount on the labelled price. He sold the suitcase for Rs 2880 with 20% profit on the labelled price .At what price did he buy the suitcase?
Sol: let the labelled price be Rs x
then 120% of x=2880
x=(2880*100)/120=Rs 2400
C.P=85% of the 2400
(85*2400)/100=Rs 2040
5.A tradesman gives 4% discount on the marked price and gives article free for buying every 15 articles and thus gains 35%.The marked price is above the cost price by
Sol: let the C.P of each article be Rs 100
then C.P of 16 articles=Rs (100*16)=Rs 1600
S.P of 15 articles =1600*(135/100)=Rs 2160
S.P of each article =2160/15=Rs 144
If S.P is Rs 96, marked price =Rs 100
If S.P is Rs 144,marked price =(100/96)*144=Rs 15000
therefore marked price=50% above C.P
6.By selling 33m of cloth ,one gains the selling price of 11m.Find the gain percent?
Sol: gain=S.P of 33m-C.P of 33m
=11m of S.P
S.P of 22m=C.P of 33m
let C.P of each meter be Rs 1,then C.P of 22m=Rs 22
S.P of 22m=Rs 33
gain=S.P-C.P=33-22=Rs 11
gain%=(gain/C.P)*100
=(11/22)*100=50%
7.The price of a jewel, passing through three hands, rises on the whole by 65%.if the first and second sellers earned 20% and 25% profit respectively,find the percentage profit earned by the third seller?
Sol: let the original price of the jewel be Rs P and
let the profit earned by the third seller be x%
then (100+x)% of 125% of P=165% of P
[(100+x)/100]*(125/100)*(120/100)*P=(165/100)*P
100+x=(165*100*100)/(125*120)
100+x=110
x=10%
8.When a producer allows 36% commission on the retail price of his product ,he earns a profit of 8.8%.what would be his profit percent if the commission is reduced by 24%
Sol: let retail price =Rs 100
commission=Rs 36
S.P=retail price-commission=100-36=Rs 64
But profit=8.8%
C.P=(100*C.P)/(gain+100)=(100*64)/(100+8.8)=Rs 1000/17
new commission=Rs 12
new S.P=100-12=Rs 88
gain=88-(1000/17)=Rs 496/17
gain%=gain*100/C.P
=(496*17*100)(17*1000)
gain%=49.6%
9.Vikas bought paper sheets for Rs 7200 and spent Rs 200 on transport. Paying Rs 600,he had 330 boxes made,which he sold at Rs 28 each. His profit percentage is
Sol: total investments=7200+
