# How will the quotient of two numbers change if the dividend is increased by 40% and the divisor is decreased by 30%

Theoretical substantiation of the problem
a: c = b, where a is the dividend, c is the divisor, b is the quotient.

Let’s denote the dividend by the letter a, and the divisor by the letter c.

Then their quotient will be equal to a: c.

Let’s increase the dividend by 40% and get: a + 40% = a * (100 + 40): 100 = 1.4 * a.

Reduce the divisor by 30% and get: s – 30% = s * (100 – 30): 100 = 0.7 * s.

Let’s find the quotient of the obtained numbers: 1, 4 * a: 0, 7 * c = 2 * a: c.

Thus, the quotient of these two numbers will double.

Answer: the quotient of two numbers, if the dividend is increased by 40% and the divisor is reduced by 30%, it will double.

Practical solution to the problem
Let’s try to solve our problem using the selection:

100: 100 = 1;
40% of 100 = 40;
30% of 100 = 30;
(100 + 40): (100 – 30) = 140: 70 = 2;
2: 1 = 2 (times)
Let’s check by substituting other numbers in place of the dividend and divisor:

200: 100 = 2;
40% of 200 = 80;
30% of 100 = 30;
(200 + 80): (100 – 30 = 280: 70 = 4;
4: 2 = 2 (times)
Answer: the quotient of two numbers, if the dividend is increased by 40% and the divisor is reduced by 30%, it will double. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.