Question

the ratio o f two numbers is 7:10 and their difference is 105​

Answer 1

Step-by-step explanation:

The ratio of two numbers is 7:10 and their difference is 105. What are the numbers?

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Don’t use pen or paper to solve these types of questions as you’ll waste more time and energy. I’m doing the following thing mentally to come up with answer in 5 seconds.

The difference between numbers is 105 ——(1)

The difference between ratio of numbers is 10–7=3 ——(2)

Divide (1) by (2)

105/3 = 35

Multiply both terms of the ratio by 35 to get the numbers

35*7/35*10 = 245/350

The numbers are 245 and 350

If you find it difficult to find 35*7 then find 35* (10–3) = 35*10 - 35*3 = 350- 105 =245

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Let those two numbers be x and y

Ratio is 7:10

x/y = 7/10

10x = 7y ———-(1)

[y = 10x/7 ]

Also it is given that,

Either x - y = 105 or y - x = 105

But from equation (1) it is clear that “y” must be a bigger number than “x” because x is multiplied 10 times to get equal to 7 times y.

So,

Valid equation will be:

y - x = 105 ————-(2)

10x/7 - x = 105 ( from equation 1 )

10x - 7x = 735

3x = 735

x = 245

Put x = 245 in equation (2)

y - 245 = 105

y = 350

Ans. X = 245 and Y = 350

Answer 2

Step-by-step explanation:

given

ratio of two numbers 7:10

and difference=105

calculation

let the numbers are 7X and 10X ( here ratio

7:10)

then 10X-7X = 105

or 3X = 105

or X = 35

then the number are (35×7)=245 and (35×10) = 350