Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 9 Commercial Mathematics Ex 9.1 Questions and Answers.

## Maharashtra State Board 11th Commerce Maths Solutions Chapter 9 Commercial Mathematics Ex 9.1

Question 1.

Find 77% of 580 + 34% of 390.

Solution:

Question 2.

240 candidates appeared for an examination, of which 204 passed. What is the pass percentage?

Solution:

We find the pass percentage using the unitary method

∴ The pass percentage for the examination is 85%.

Question 3.

What percent of 8.4 kg are 168 grams?

Solution:

Let 168 gms be x% of 8.4 kg

i.e., let 168 gms be \(\frac{x}{100}\) of 8400 gms

∴ 168 = \(\frac{x}{100}\) × 8400

∴ x = \(\frac{168}{84}\) = 2

∴ 168 gms is 2% of 8.4 kg.

Question 4.

If the length of a rectangle is decreased by 20%, what should be the increase in the breadth of the rectangle so that the area remains the same?

Solution:

Let x and y represent the length and breadth of the rectangle respectively.

∴ The original area of the rectangle = xy

There is a 20% decrease in length.

Let k % be the required increase in breadth

Given that the new and old areas should be equal.

∴ 100 + k = 125

∴ k = 125 – 100 = 25

∴ Breadth should be increased by 25% so that the area remains same.

Question 5.

The price of rice increased by 20%, as a result, a person can have 5kg rice for ₹ 600. What was the initial price of rice per kg?

Solution:

A person can buy 5 kg of rice for ₹ 600 after the increase in price

∴ New price of rice = \(\frac{600}{5}\) = ₹ 120/kg …..(i)

Let ‘x’ be the initial price per kg of rice.

There is a 20% increase in the price of rice.

Thus the new price of the rice will be given as

∴ The initial price of rice is ₹ 100 per kg

Question 6.

What percent is 3% of 5%?

Solution:

Let 3% be x % of 5%.

Then \(\frac{3}{100}=\frac{x}{100} \times \frac{5}{100}\)

∴ x = \(\frac{3 \times 100}{5}\) = 60

∴ 3% is 60% of 5%.

Question 7.

After availing of two successive discounts of 20% each, Madhavi paid ₹ 64 for a book. If she would have got only one discount of 20%, how much additional amount would she have paid?

Solution:

Let the price of the book be ₹ x.

After the first 20% discount, the price of the book becomes

After another 20% discount, the price of the book becomes

This price = ₹ 64 …..[Given]

∴ \(\frac{16}{25}\)x = 64

∴ x = 4 × 25 = 100

Thus, Amount of the book after one discount = \(\frac{4}{5}\)(100) = 80 …..[from (i)]

∴ The additional amount that Madhavi would have paid = 80 – 64 = ₹ 16

Question 8.

The price of the table is 40% more than the price of a chair. By what percent price of a chair is less than the price of a table?

Solution:

Let ₹ x and ₹ y be the price of a table and chair respectively.

The price of the table is 40% more than the price of a chair

∴ \(\frac{x-y}{y}\) × 100 = 40

We need to find by how much percent is the price of a chair less than that of a table.

∴ The price of a chair is 28.57% less than the price of a table.

Question 9.

A batsman scored 92 runs which includes 4 boundaries 5 sixes. He scored other runs by running between the wickets. What percent of his total score did he make by running between the wickets?

Solution:

Batsman scores 4 fours (boundaries) and 5 sixes in 92 runs.

Number of runs scored by fours and sixes = 4 × 4 + 5 × 6 = 46

∴ 92 – 46 = 46

Let 46 be x% of 92.

Then 46 = \(\frac{x}{100}\) × 92

∴ x = \(\frac{46 \times 100}{92}=\frac{100}{2}\) = 50

∴ 50% of the total runs were scored by running between the wickets.