**1) **
**What will be % profit aftrr selling an article at a certain price if there is a loss of 45% when the article sold at 1/3 of prrvious price??(Srinivas)**

**Ans.**
**Shortcut by Rajat**

**55×3=165**
**165-100=65**
**Shortcut by Divya**

**Cp = 100**
**1/3 sp = 55**
**Sp = 165**

**=> 65%**

**=========================**

**2.A profit of 20% is made on goods when a discount of 10% is given on the market price. What profit percent will be made when a discount of 20% is given on the market price?**

**Ans.**

**Shortcut by Rajat**

**120/90 ×80=320/3=106.67**
**Shortcut by Divya**

**120 = 90**
**?? = 80**

**Shortcut by Chauhan**

**Mp-100**
**Sp-90**
**Cp-75**

**New**
**Mp-100**
**Sp-80**
**P=80-75=5**
**5*100/75=20/3**

**=======================**

**3.The profit percentage of A and B are the same on selling the articles at 2400 rs each but A calculates his profit on the selling price while B calculates it on the cost price. This profit is equal to 23% each. What is the difference between their profits?**

**Ans.**

**Shortcut by Divya**

**Profit = profit% / cp for 1st**
**Profit = profit% / sp fpr 2nd**
**2400 ( 23/100 - 23/123)**

**Shortcut by Rajat**
**first 2400×23% =552**
**second 2400/123 ×23=448 aprx**

**========================**

**4.solve for X and Y? (Divya)**

**1.1x+1.25y=760**
**1.25x+1.1y=767.5**

**Ans.**

**Solution by (Perfect,vikas,divya,deepak)**

**110 x+125y=76000**
**125x +110y=76750**

**Subtract**

**X-y=50**

**Put in 1**

**110(50+y)+125y=76000**

**On solving y=300110 x + 125y =76000**

**125x +110y=76750**

**Subtract**
**X-y=50**

**Put in 1**

**110(50+y)+125y=76000**
**On solving y=300**

**===================**
**5.Rakesh calculates his profit % on the selling price where as ramesh calculates his on the cost price they find that the differance of their profits is 100. If the selling price of both of them are same and both of them get 25% profit, find their selling price?**

**Ans.**

**Shortcut by Divya**

**25/100 - 25/125 = 1/20**

**20*100 = 2000**

**--------**
**Shortcut by Vikas Awasthi**

**100....75**
**100....80**

**5=100**
**100=2000**

**Shortcut by Vaibhav**

**x*25%-x*25/125=100 given**
**5=100**
**100=2000**
**===========================**

**6.An article is sold at a profit of 10%. If Selling Price and purchase price both are less by Rs.25/-, then profit will be 5% more. Find purchase price of an article?**

**Ans. Solved by divya**

**(x-25)*1.15 = 1.1x-25**

**Solve x**

**X=75**

**-----------**

**Solved by Vikas Awasthi**

**25*0.15/0.05)=25*3=75**

**-------**

**Solved by PERFECT**

**10 0**
** 15**
**15 5**

**3 : 1 (15, 5 ratio)**

**1---------25**
**3--------75**

**======================**

**7.Two partners invested 1250 rs and 850 rs respectively in a business. Both the partners shared 60% of the profit and distributed the rest 40% as the interest on their capittals. If one partner received 30 rs more than the other , the total profit is ?**

**Ans.**
**Solution by Vikas Awasthi**

**60% main equl= 30&30**

**In 40% 25:17 so 23.81 & 16.19**

**So % prft for both= (30+23.81]&(30+16.19)=53.81% & 46.19%**

**Diff=7.62%**

**7.62%=30**
**100=393.7**

**#crct me if i am wrng**

**------------------**

**Solution by Vaibhav**

**Let Profit be x**

**60%x= 3/5x**

**(3/5x*25/42)-(35x*17/42)=30**

**262.50**
**--------------------**

**Solutoin by RR**

**Vikas solution corrected by Atul**

**30+30 wrong**

**Equally nhi krenge jab investment alag he**

**============================**

**8.Two partner invested Rs, 1,00,000 and 1,40,000 respectively in a business and agreed that 70% of the profits should be divided equally between them. and the remaining profit in the ration of their investments. If one partner gets Rs. 180 more than the other , then the total profit made in the business ? (Pooja)**

**Ans.**

**Solution by Vaibhav**

**========================**

**9.A tradesman sold an article at a loss of 20% . Had he sold it for Rs. 100 more . he should hv gained 5% . The cost price of the article was? (Jitender Dagar)**

**Ans.**

**Shortcut by ~V**

**25% = 100**

**100%= 400**

**==========================**

**10.The percentage of profit, when an article is sold for Rs 78 is twice than when it is sold for Rs 69. The cost price of the article is? (Mala Singh)**

**Ans.**

**Shortcut by Krish**

**Let c.p=x**

**(78 - x)/x = 2(69 - x)/x**

**x=60**

**Shortcut by ~V**

**78-69= 9**

**69-9= 60**

**==========================**

**11.In an office of 90 employees, amongst 50% of them each **

**employee got number of sweets that are 20% of the total number of employees and the amongst remaining 50% of the employees each employee got number of sweets that are 10% of the total number of employees. How many sweets were distributed among 90 employees? (Mala Singh)**

**Ans.**

**Shortcut by Rajat Sharma**

**45×18+45×9**

**1215**

**=======================**

**12.How many degrees are there in an angle which equals one-fifth of its supplement? (Vaibhav)**

**Ans.**

**Shortcut by Divya **

**x = 1/5(180-x)**

**x=30**

**---------**

**Shortcut by ~V**

**X+5X=180**

**X=30**

**=======================**

**13.A sum of rs. 16400 was taken at the rate of 5% compounded annually to be paid back in two equal annual instalments. Find the two instalments?**

**Ans.**

**Shortcut by Rajat Sharma**

**16400×1.05=17220**

**now divide 17220 in 105:100 **

**105 wali value installment hogi**

**105/205*17220=8820**

**========================**

**14.Pipe A and B can fill a tank in 10 hours and 8 hours respectively. A pipe C can empty the full tank in 40 hours. All the three pipes were opened for 3 hours after which pipe C was turned off. Find the dofference in the time required now and time required , had pipe C not opened? (Akash Sonkusare)**

**Ans.**

**Solution by Rajat**

**look **

**a 10**

**b 8 **

**c 40 **

**LCM 40 **

**1 hour work**

**a=4**

**b=5**

**c=-1 **

**all three did work in 3 hour=8×3=24 **

**left 16 **

**now c left reuired time now=16/9**

**when only a and b worked **

**they did in 3 hour=9×3=27**

**left work=13**

**required time now=13/9**

**diff=16/9-13/9=3/9=1/3**

**==========================**

**15.A person bought some oranges worth rs 36 from each of the five markets at rs 1 , rs 1.5 , rs . 1.8 , rs 2 and rs 2.25 per orange respectively. What is the average price of an orange? (Mathi)**

**Ans.**

**Solution by Rajat Sharma**

**36/1+36/1.5+36/1.8+36/2+36/2.25=36+24+20+18+16**

**=114 orange**

**and **

**amount=36×5=180**

**rate=180/114 × 100=1.57 aprx**

**==============**

**16.A cistern has three pipes A B and C .the pipes A and B can fill it in 4 snf 5 hours respectively and C can empty it in 2 hours .if the pipes are opened in an order 1 , 2, and 3 am , when will the cistern be empty? (Akash Sonkusare)**

**Ans.**

**Solution by Rajat**

**a 4**

**b5**

**c 2**

**LCM 20 **

**one hour work**

**a 5**

**b 4**

**c -10 **

**now from 1 to 2 am **

**a completed 5 unit ...**

**from 2 to 3 am a and b completed 9 unit **

**at 3 am total 5+9=14 unit completed **

**now a b and c will work **

**then they will empty 1 unit per hour **

**so required hour=14/1=14**

**At 3 am 14 unit full **

**onwards 1 uNit emptied **

**3 am +14 hour=5 pm**

**=======================**

**17.If 30% loss on sp an article makes the trader to suffer a loss of rs 45 then find the sp ? (Rajat Sharma)**

**Ans.**

**Solution by Vikas Awasthi**

**Let SP=100**

**Loss**

**30% on Sp=70**

**70=100**

**100=142.86(CP)**

**142.86-100=42.86% actually loss**

**42.86=45**

**100=105**

**If 100 is SP den we hev to find CP**

**30% of SP is Loss**

**Then 100% of SP=CP**

**-----------------**

**Solution by Reea**

**Let SP=100 Loss**

**30% on Sp=70**

**70=100**

**100=142.86(CP)**

**142.86-100=42.86% actually loss**

**42.86=45**

**100=105**

**--------------**

**Shortcut by Rohit Tiwari**

**Loss/loss% = saleprice/100-loss**

**45/30 = sp/70**

**Sp = 105**

**======================**

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