AP State Syllabus AP Board 7th Class Maths Solutions Chapter 6 Ratio – Applications Ex 5 Textbook Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 6th Lesson Ratio – Applications Exercise 5

Question 1.

A shopkeeper bought a suit case for ₹ 480 and sold it for ₹ 540. Find his gain percent?

Solution:

C.P of the suitcase = ₹ 480

SP of the suitcase = ₹ 540

∴ gain=S,P-C.P = 540 – 480 = ₹ 60

∴ gain percent = \(\frac { 60 }{ 450 }\) × 100% = 12.5%

Question 2.

Ajay bought a TV for ₹ 15000 and sold it for ₹141 00. Find the loss percent?

Solution:

C.P of the TV = ₹ 15,000

S.P of the TV = ₹ 14100

As S.P < C.P

Loss = C.P – S.P= 15,000 – 14,100 = ₹ 900

∴ Loss percent = \(\frac { 900 }{ 15000 }\) × 100 = 6%

Question 3.

Ramu sold a plot of land for ₹ 2,40,000 gaining 20%. For how much did he purchase the plot?

Solution:

Let the cost price of the land = ₹ x

gain percent = 20% of the C.P

∴ S.P of the land = 120% of C.P

By problem, 120% of x = 2,40,000

\(\frac { 120. x }{ 100 }\) = 2,40,000

x = 2.40000 × \(\frac {100 }{ 120 }\)

= ₹ 2,00,000

(OR)

Let the C.P of the land = ₹ x

gain percent = 20% of C.P = 20% of x = \(\frac{20 \mathrm{x}}{100}\)

∴ S.P of the land = C.P + gain

= x + \(\frac{20 \mathrm{x}}{100}\)

= \(\frac{100 x+20 x}{100}=\frac{120 x}{100}\)

By problem, \(\frac{20 \mathrm{x}}{100}\) = 2,40.000

∴ x = 24000 x \(\frac { 100 }{ 120 }\)

= ₹ 2,00,000

Question 4.

On selling a mobile for ₹ 750, a shop keeper looses 10%. For what amount should he sell it to gain 5%?

Solution:

Let the C.P of the mobile be x

Losspercent = 10% of C.P = 10% of x = \(\frac{10 \mathrm{x}}{100}\)

∴ Loss = \(\frac{10 x}{100}\)

∴ S.P = C.P – Loss

= \(x – \frac{10 x}{100}=\frac{100 x-10 x}{100}=\frac{90 x}{100}\)

By problem, \(\frac{90 \mathrm{x}}{100}\) = 750

x = 750 × \(\frac { 100 }{ 90 }\) = ₹ \(\frac { 2500 }{ 3 }\)

Now to gain by 5% the S.P = C.P + 5% of C.P

Question 5.

A farmer sold 2 bullocks for ₹ 24000 each. On one bullock he gained 25% and on the other he lost 20%. Find his total profit or loss percent?

Solution:

Let the C.P of first bullock be x

gain = 25% of x = 25 × \(\frac{x}{100}=\frac{25 x}{100}\)

S.P = C.P + gain = x + \(\frac{25 x}{100}=\frac{100 x+25 x}{100}=\frac{125 x}{100}\)

Selling price of first bullock 24,000 (given)

\(\frac{125 x}{100}\) = 24000

x = \(\frac{24000}{125}\) × 100

∴ C.P of first bullock = ₹ 19.200

Let the C.P of second bullock be y

Loss percent = 20%

∴Loss = \(\frac{20 \times \mathrm{y}}{100}=\frac{20 \mathrm{y}}{100}\)

S.P = C.P – loss

= \(y-\frac{20 y}{100}=\frac{100 y-20 y}{100}=\frac{80 y}{100}\)

But S.P = ₹ 24,000 (given)

\(\frac{80 \mathrm{y}}{100}\) = 24,000

∴ y = 24000 x \(\frac{100}{80}\) = 30,000

∴ C.P of second bullock = ₹ 30,000

C.P of 2 bullocks = ₹19,200 + ₹30,000

= ₹ 49,200

S.P of 2 bullocks ₹24,000 × 2 = ₹48,000

Loss = C.P – S.P = 49,200 – 48,000 = ₹1200

Loss % = \(\frac{\text { loss }}{\text { CP }}\) × 100

= \(\frac{1200}{49200}\) × 100 = 2.4

∴ Loss% = 2.4%

Question 6.

Sravya bought a watch for ₹480. She sold it to Ridhi at a gain of 6\(\frac { 1 }{ 4 }\) %. Ridhi sold it to Divya at a gain of 10%. How much did Divya pay for it?

Solution:

CF of the watch = ₹ 480

Gain% = \(6 \frac{1}{4} \%=\frac{25}{4} \%\)

Gain = 480 × \(\frac{25}{4}\) x \(\frac{1}{100}\) = 30

C.P of the watch for Ridhi = 480 + 30 = ₹ 510

Gain% = 10%

∴ Gain= 51% × \(\frac{10}{100}\) = 51

S.P of the watch for Ridhi = 510 + 51 = ₹561

∴ Amount paid for Divya for the watch = ₹561

Question 7.

The marked price of a book is ₹225.Thc publisher allows a discount of ₹10% on it. Find the selling price of it?

Solution:

The marked price of the book = ₹ 225

Discount 10%

∴ Discount = 225 × \(\frac{10}{100}\)= ₹ 22.5

S.P = M.P – discount

= 225 – 22.5 = ₹202.5

∴ Selling price of the book = ₹ 202.5

Question 8.

A carpenter allows 15% discount on his goods. Find the marked price of a chair which is sold by him for ₹680?

Solution:

Let the marked price of chair be ₹x

Discount = 15% = x × \(\frac{15}{100}=\frac{15 x}{100}\)

S.P = M.P – discount

\(x-\frac{15 x}{100}=\frac{100 x-15 x}{100}=\frac{85 x}{100}\)

S.P = ₹ 680 (given)

∴ \(\frac{85 \mathrm{x}}{100}\) = 680

x = \(\frac{680 \times 100}{85}\) = 800

Marked price of the chair = ₹ 800

Question 9.

A dealer allows a discount of ₹ 10% and still gains by 10%. What should be the marked price if the cost price is ₹900?

Solution:

Given that C.P = 900

There is a gain of 10% on C.P

∴ Gain = 10% of ₹ 900

= \(\frac{10 \times 900}{100}\) = ₹ 90

∴ S.P = C.P . gain

= 900 + 90

S.P = ₹990 …………….. (1)

Let the marked price = ₹ x

Discount on it = 10% on M.P = \(\frac{10 \mathrm{x}}{100}\)

∴ Selling Price = MP – Discount

= x – \(\frac{10 \mathrm{x}}{100}\)

= \(\frac{100 x-10 x}{100}\)

∴ S.P = \(\frac{90 \mathrm{x}}{100}\) …………….(2)

From (1) & (2) \(\frac{90 \mathrm{x}}{100}\) = 990

∴ x = 990 x \(\frac{100}{90}\)

∴ M.P = x = ₹1100