Question

The sum of two number is 2490 and if 6.5% of one number is equal to
8.5% of the other, then numbers are.
(A) 1414, 1076
(C) 1412, 1078
(B) 1411, 1079
(D) None of these​

Answer 1

Answer:

(B) 1411, 1079

Step-by-step explanation:

It is given that 6.5% of one number is equal to 8.5% of the other. So, we can conclude that the numbers are in the ratio 6.5:8.8 i.e. 65:85. This ratio can be written as 13:17. So, sum of two numbers is 2490 and their ratio is 13:17.

13x+17x=2490

30x=2490

x=2490/30

x=83

Numer= 13x=13(83)=1079

=17x=17(83)=1411

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Answer 2

Given

• Sum of two numbers is 2490.
• 6.5% of one number= 8.5% of other.

To find

• The Numbers

Let the two numbers be x and y .

So,

$\sf→x+y=2490 \: \: \: \: \: \: - - - - (1)$

Now it is given that,6.5% of one number is equal to 8.5 of other.

$\\\sf→6.5\% \: of\: x= 8.5\%\: of \: y$

$\sf→ \cfrac{6.5}{100} \: \times \: x= \cfrac{8.5}{100} \: \times \: y$

$\sf→ 6.5x \times 100 \: = 8.5y \times 100$

$\sf→ 650x \: = 850y$

$\sf→ 65 \cancel{0}x \ \: = 85 \cancel0y$

$\sf→ x \ = \cfrac{85y}{ 65 \: \: }$

$\sf→ x \ = \cfrac{17y}{ 13\: \: }$

Now , putting the Value of x in Equation 1 We get

$\\\sf→ \cfrac{17y}{13 \: \: } +y=2490$

$\sf→ \cfrac{17y + 13y}{13 \: \: } =2490$

$\sf→ {30y}{ } =2490 \times 13$

$\sf→ y= \cfrac{ 32370}{30}$

$\sf→ y=1079$

On putting the Value of y in Equation 1 We get

$\\\sf→x+1079=2490$

$\sf→x=2490 - 1079$

$\sf→x=1411$

• Hence,the numbers are 1079 and 1411.