5 Mark Question

Question 15 Marks

Saritaben, Ayesha and Meenakshi started a business by investing Rs 2400, Rs 5200 and Rs 3400. They made a profit of 50%. If they reinvested all their profit by adding it to the capital, find out the proportions of their shares in the capital during the following year.

Answer

Total investment $=$ Rs $2400+$ Rs $5200+$ Rs $3400=$ Rs 11000
Total profit $=50 \%$ of $11000=\frac{50}{100} \times 11000=$ Rs 5500
Proportion of shares $=2400: 5200: 3400$
$=12: 26: 17 \ldots$ (Dividingby 200 )
Let the profit of Saritaben, Ayesha and Meenakshi be Rs 12x, Rs 26x and Rs $17 x$ respectively.
$12 x+26 x+17 x=5500$
$\therefore 55 x=5500$
$\therefore x=100$
$\therefore$ Saritaben's profit $=12 x =12 \times 100=$ Rs 1200
Ayesha's profit $=26 x=26 \times 100=$ Rs 2600
Meenakshi's profit $=17 x =17 \times 100=$ Rs 1700
$\therefore$ Saritaben's new investment $=2400+1200=$ Rs 3600
Ayesha's new investment $=5200+2600=$ Rs 7800
Meenakshi's new investment $=3400+1700=$ Rs 5100
$\therefore$ New proportion of shares $=3600: 7800: 5100$
$=12: 26: 17 \ldots$ (Dividing by 300 )
$\therefore$ The proportion of the shares in the capital during the following year is $12: 26: 17$

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Question 25 Marks

Can you give examples from science or everyday life of quantities that vary in direct proportion ?

Answer

Number of chairs and the number of spectators.
Quantity (litres) of water and number of vessels required to store the water.

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Question 35 Marks

Are the amount of petrol filled in a motorcycle and the distance traveled by it, in direct proportion ?

Answer

Yes.
If amount of petrol filled in the motorcycle is less, it will travel less distance and if the amount of petrol filled is more, it will travel more distance.
Hence, the amount of petrol filled in the motorcycle and the distance traveled by it are in direct proportion.

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Question 45 Marks

Saritaben, Ayesha and Meenakshi started a business by investing Rs 2400, Rs 5200 and Rs 3400. They made a profit of 50%. If they reinvested all their profit by adding it to the capital, find out the proportions of their shares in the capital during the following year.

Answer

Total investment $=$ Rs $2400+$ Rs $5200+$ Rs $3400=$ Rs 11000
Total profit $=50 \%$ of $11000=\frac{50}{100} \times 11000=$ Rs 5500
Proportion of shares $=2400: 5200: 3400$
$=12: 26: 17 \ldots$ (Dividingby 200 )
Let the profit of Saritaben, Ayesha and Meenakshi be Rs 12x, Rs 26x and Rs $17 x$ respectively.
$12 x+26 x+17 x=5500$
$\therefore 55 x=5500$
$\therefore x=100$
$\therefore$ Saritaben's profit $=12 x =12 \times 100=$ Rs 1200
Ayesha's profit $=26 x=26 \times 100=$ Rs 2600
Meenakshi's profit $=17 x =17 \times 100=$ Rs 1700
$\therefore$ Saritaben's new investment $=2400+1200=$ Rs 3600
Ayesha's new investment $=5200+2600=$ Rs 7800
Meenakshi's new investment $=3400+1700=$ Rs 5100
$\therefore$ New proportion of shares $=3600: 7800: 5100$
$=12: 26: 17 \ldots$ (Dividing by 300 )
$\therefore$ The proportion of the shares in the capital during the following year is $12: 26: 17$

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Question 55 Marks

Jaya, Seema, Nikhil and Neelesh put in altogether Rs 360000 to form a partnership, with their investments being in the proportion 3 : 4 : 7 : 6. What was Jaya’s actual share in the capital? They made a profit of 12%. How much profit did Nikhil make ?

Answer

Total investment $=$ Rs 360000
Profit earned $=12 \%$
$\therefore$ Total profit $=12 \%$ of 360000
$=\frac{12}{100} \times 360000=$ Rs 43200
Proportion of investment $=3: 4: 7: 6$
Let the investment of Jaya, Seema, Nikhil and Neelesh be Rs $3 x$, Rs $4 x$, Rs $7 x$ and Rs $6 x$ respectively.
$
\begin{aligned}
& 3 x +4 x +7 x +6 x =360000 \\
& \therefore 20 x =360000 \\
& \therefore x=\frac{360000}{20} \\
& =18000 \\
& \therefore \text { Jaya's investment }=3 x =3 \times 18000=\text { Rs } 54000
\end{aligned}
$
Also, profit made by them is Rs 43200
$
\begin{aligned}
& \therefore 3 x +4 x +7 x +6 x =43200 \\
& \therefore 20 x =43200 \\
& \therefore x=\frac{43200}{20} \\
& =2160
\end{aligned}
$
$\therefore$ Nikhil's profit $=7 x=7 \times 2160=$ Rs 15120
$\therefore$ Jaya's share in the capital was Rs 54000 and the profit made by Nikhil was Rs 15120 .

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Question 65 Marks

A and B shared a profit of Rs 24500 in the proportion 3 : 7. Each of them gave 2% of his share of the profit to the Soldiers’ Welfare Fund. What was the actual amount given to the Fund by each of them ?

Answer

Proportion of share $=3: 7$
Let the profits of $A$ and $B$ be Rs $3 x$ and Rs $7 x$ respectively.
$
\begin{aligned}
& 3 x +7 x =24500 \\
& \therefore 10 x =24500 \\
& \therefore x=\frac{24500}{10}=2450
\end{aligned}
$
Profit earned by $A=3 x=3 \times 2450=$ Rs 7350
Amount given by $A=2 \%$ of his profit
$
=\frac{2}{100} \times 7350=\text { Rs } 147
$
Profit earned by $B=7 x=7 \times 2450=$ Rs 17150
Amount given by $B=2 \%$ of his profit
$
=\frac{2}{100} \times 17150=\text { Rs } 343
$
$\therefore$ The amount given by $A$ and $B$ to the Soldiers' Welfare Fund are Rs 147 and Rs 343 respectively.

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Question 75 Marks

Shweta, Piyush and Nachiket together invested Rs 80000 and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was Rs 30000 and Piyush’s Rs 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of the profit ?

Answer

Total investment $=$ Rs 80000
Nachiket's investment $=$ Total investment - (Shweta's investment +
Piyush's investment)
$
\begin{aligned}
& =80000-(30000+12000) \\
& =80000-42000=\text { Rs } 38000
\end{aligned}
$
Profit earned $=24 \%$
$\therefore$ Total profit $=24 \%$ of $80000=\frac{24}{100} \times 80000=$ Rs 19200
Proportion of investment $=30000: 12000: 38000$
$=15: 6: 19 \ldots$ (Dividing by 2000 )
Let the profit of Shweta, Piyush and Nachiket be Rs $15 x$, Rs $6 x$ and Rs $19 x$ respectively.
$
\begin{aligned}
& 15 x +6 x +19 x =19200 \\
& \therefore 40 x =19200 \\
& \therefore x=\frac{19200}{40}=480
\end{aligned}
$
$\therefore$ Nachiket's profit $=19 x=19 \times 480=$ Rs 9120
$\therefore$ Nachiket's investment is Rs 38000 and his profit is Rs 9120 .

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Question 85 Marks

Virat and Samrat together invested Rs 50000 and Rs 120000 to start a business. They suffered a loss of 20%. How much loss did each of them incur ?

Answer

Total investment $=$ Rs $50000+$ Rs $120000=$ Rs 170000
Loss incurred $=20 \%$
$\therefore$ Total loss $=20 \%$ of $170000=\frac{20}{100} \times 170000=$ Rs 34000
Proportion of investment $=50000: 120000$
$=5: 12 \ldots$ (Dividingby 10000 )
Let the loss incurred by Virat be Rs $5 x$ and that by Samrat be Rs $12 x$.
$5 x+12 x=34000$
$\therefore 17 x =34000$
$\therefore x=\frac{34000}{17}=2000$
$\therefore$ Virat's loss $=5 x =5 \times 2000=$ Rs 10000
Samrat's loss $=12 x=12 \times 2000=$ Rs 24000
$\therefore$ The loss incurred by Virat and Samrat are Rs 10000 and Rs 24000 respectively.

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Question 95 Marks

Suresh and Ramesh together invested Rs 144000 in the ratio 4 : 5 and bought a plot of land. After some years they sold it at a profit of 20%. What is the profit each of them got ?

Answer

Total investment $=$ Rs 144000
Profit earned $=20 \%$
$\therefore$ Total profit $=20 \%$ of $144000=\frac{20}{100} \times 144000=$ Rs 28800
Proportion of investment of Suresh and Ramesh $=4: 5$
Let the profit of Suresh be Rs $4 x$ and that of Ramesh be Rs $5 x$.
$4 x +5 x =28800$
$\therefore 9 x =28800$
$\therefore x=\frac{28800}{9}$
$=3200$
$\therefore$ Suresh's profit $=4 x=4 \times 3200=$ Rs 12800
Ramesh's profit $=5 x=5 \times 3200=$ Rs 16000
$\therefore$ The profit earned by Suresh and Ramesh are Rs 12800 and Rs 16000 respectively.

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Maths 5 Mark Question

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