# 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.