Question

1) Tanishk sold two books for ₹600 each, thereby gaining 20% on one book and losing 20% on the other book. Find his overall loss or gain per cent.

2) Attached.

Note:-
•Solve the both the sums.
•Spam answers will be reported.
•Correct answer will be appreciated :)
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Answer 1

1) Tanishk sold two books for ₹600 each, thereby gaining 20% on one book and losing 20% on the other book. Find his overall loss or gain percent.

• Answer: Tanishk's loss is 4%.

• Step-by-step explanation:

Selling price of the first book = ₹600

Its profit = 20%

$\:\:\:\:\:\:\implies{\sf{C.P=\frac{100\times S.P}{(100+Profit\: percentage)}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\frac{100\times 600}{100+20}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\frac{6000\cancel{0}}{12\cancel{0}}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\frac{6000}{12}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\underline{\underline{500/-}}}}$

Selling price of second book = ₹600

Its loss = 20%

$\:\:\:\:\:\:\implies{\sf{C.P=\frac{100\times S.P}{(100-Loss\: percentage)}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\frac{100\times 600}{100-20}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\frac{6000\cancel{0}}{8\cancel{0}}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\frac{6000}{8}}}$

$\:\:\:\:\:\:\:\:\:\:{\sf{=\underline{\underline{750/-}}}}$

$\sf{So,}$

The total cost price of the books:

$\:\:\:\:\rightarrow{\sf{500+750}}$

$\:\:\:\:\rightarrow{\sf{\underline{1250/-}}}$

The total selling price of the books:

$\:\:\:\:\rightarrow{\sf{600+600}}$

$\:\:\:\:\rightarrow{\sf{\underline{1200/-}}}$

★ As the total selling price of the books is lesser than the total cost price of the books, there is a loss.

$\:\:\:\:\:\:\underline{\boxed{\sf{Loss=(C.P - S.P)}}}$

$\longrightarrow{\sf{1250-1200}}$

$\longrightarrow{\sf{\underline{\underline{50/-}}}}$

As per the question, now we've to find the loss (%).

$\:\:\:\:\:\:\underline{\boxed{\sf{{Loss}_{(Percentage)}=\frac{Loss}{C.P}\times 100}}}$

$\longrightarrow{\sf{\frac{50}{125\cancel{0}}\times 10\cancel{0}}}$

$\longrightarrow{\sf{\frac{50\times 10}{125}}}$

$\longrightarrow{\sf{\frac{500}{125}}}$

$\longrightarrow{\underline{\underline{\sf{\red{4\%}}}}}$

${\boxed{\sf{\therefore Tanishk's \:loss\:is\:4\%.}}}$

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2) Naresh, Gopi and Sarath started a business with investments of ₹10,000, ₹20,000 and ₹20,000 respectively. After 6 months, Gopi withdrew an amount of ₹5,000 from his investment. After 3 more months, Sarath added ₹10,000 to his investment. If at the end of the year, the total profit earned is ₹36,000, then find the share of each.

• Answer:

1. Naresh's share = ₹7,200
2. Gopi's share = ₹12,600
3. Sarath's share = ₹16,200

• Step-by-step explanation:

★${\boxed{\sf{Naresh}}}$

• Investment = ₹10,000
• Period of investment = 12 months

$\implies$ Total investment made by him = $\sf{\underline{(12\times 10,000)/-}}$ - - - - - - - - - ${\boxed{\sf{1}}}$

★${\boxed{\sf{Gopi}}}$

• Investment = ₹20,000
• Period of investment = 6 months
• Amount withdrawn = ₹5,000

$\implies$ Investment of remaining 6 months = $\sf{(20,000-5,000)=15,000/-}$

$\implies$ Total investment made by him = $\sf{\underline{(6\times 20,000 + 6\times 15,000)}}$ - - - - - - - ${\boxed{\sf{2}}}$

★${\boxed{\sf{Sarath}}}$

• Investment = ₹20,000
• Period of investment = 9 months (6+3)
• Added investment = ₹10,000

$\implies$ Investment for the remaining 3 months = $\sf{(20,000+10,000)=30,000/-}$

$\implies$ Total investment made by him = $\sf{\underline{(9\times 20,000 + 3\times 30,000)}}$ - - - - - - - ${\boxed{\sf{3}}}$

$\sf{Now,}$

From eqs (1), (2) and (3), we get the ratio of investments of Naresh, Gopi and Sarath respectively as:

$\:\:\:\:\:\:$$\rightarrow{\sf{(12\times 10,000):(6\times 20,000 + 6\times 15,000):(9\times 20,000 + 3\times 30,000)}}$

$\:\:\:\:\:\:$$\rightarrow{\sf{(1,20,000):(1,20,000+90,000):(1,80,000+90,000)}}$

$\:\:\:\:\:\:$$\rightarrow{\sf{(1,2\cancel{0},\cancel{0}\cancel{0}\cancel{0}):(2,1\cancel{0},\cancel{0}\cancel{0}\cancel{0}):(2,7\cancel{0},\cancel{0}\cancel{0}\cancel{0})}}$

$\:\:\:\:\:\:$$\rightarrow{\sf{12:21:27}}$

$\:\:\:\:\:\:$$\rightarrow{\sf{\underline{\underline{4:7:9}}}}$

★Total profit at the end of the year = ₹36,000

The total profit is divided in the ratio of their investments.

$\sf{Hence,}$

$\sf{Naresh's\:share=\frac{4}{20}\times 36,000=\red{\underline{7,200/-}}}$

$\sf{Gopi's\:share=\frac{7}{20}\times 36,000=\red{\underline{12,600/-}}}$

$\sf{Sarath's\: share=\frac{9}{20}\times 36,000=\red{\underline{16,000/-}}}$

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