HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

The integrating factor of the differential equation `dy/dx - y = x` is e^−x.

State whether the following is True or False:

The degree of a differential equation is the power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any.

Solve the differential equation:

`e^(dy/dx) = x`

Solve the differential equation:

dr = a r dθ − θ dr

Solve:

(x + y) dy = a² dx

Solve

`dy/dx + 2/ x y = x^2`

y2 dx + (xy + x²)dy = 0

x²y dx – (x³ + y³) dy = 0

`xy dy/dx  = x^2 + 2y^2`

 `dy/dx = log x`

y dx – x dy + log x dx = 0

An agent charges 12% commission on the sales. What does he earn if the total sale amounts to ₹ 48,000? What does the seller get?

A salesman receives 3% commission on the sales up to ₹ 50,000 and 4% commission on the sales over ₹ 50,000. Find his total income on the sale of ₹ 2,00,000.

Ms. Saraswati was paid ₹ 88,000 as a commission on the sale of computers at the rate of 12.5%. If the price of each computer was ₹ 32,000, how many computers did she sell?

Anita is allowed 6.5% commission on the total sales made by her, plus a bonus of `1/2`% on the sale over ₹ 20,000. If her total commission amounts to ₹ 3,400, find the sales made by her.

Priya gets a salary of ₹ 15,000 per month and commission at 8% on the sales over ₹ 50,000. If she gets ₹ 17,400 in a certain month, find the sales made by her in that month.

Find the area of circle x² + y² = 25.

The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. Find the percentage reduction in the value of the business.

Mr. Pavan is paid a fixed weekly salary plus commission based on a percentage of sales made by him. If on the sale of ₹ 68,000 and ₹ 73,000 in two successive weeks, he received in all ₹ 9,880 and ₹ 10,180, find his weekly salary and the rate of commission paid to him.

Deepak’s salary was increased from ₹ 4,000 to ₹ 5,000. The sales being the same, due to reduction in the rate of commission from 3% to 2%, his income remained unchanged. Find his sales.