The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.
Answer
382.8k+ views
Hint: Assume the numbers to be some variables. Form simultaneous equations as per the information given in the question and then solve them.
According to the question, the sum of two numbers is 2490.
Let the two numbers be a and b. Then we have:
$ \Rightarrow a + b = 2490 .....(i)$
Next, it is given in the question that 6.5% of one number is equal to 8.5% of other. From this we’ll get:
$
\Rightarrow \dfrac{{6.5}}{{100}} \times a = \dfrac{{8.5}}{{100}} \times b, \\
\Rightarrow 65a = 85b, \\
\Rightarrow 13a = 17b, \\
\Rightarrow a = \dfrac{{17}}{{13}}b \\
$
Putting the value of a in equation $(i)$, we’ll get:
\[
\Rightarrow \dfrac{{17}}{{13}}b + b = 2490, \\
\Rightarrow \dfrac{{30}}{{13}}b = 2490, \\
\Rightarrow b = \dfrac{{2490 \times 13}}{{30}}, \\
\Rightarrow b = 1079 \\
\]
Putting the value of b in equation $(i)$, we’ll get:
$
\Rightarrow a + 1079 = 2490, \\
\Rightarrow a = 2490 - 1079, \\
\Rightarrow a = 1411 \\
$
Thus the numbers are 1411 and 1079 respectively.
Note: Instead of assuming variables, we can directly solve the question using ratios. 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. Thus, we have to divide 2490 in the ratio 13:17.
So, our numbers will be $\dfrac{{13}}{{13 + 17}} \times 2490$ and $\dfrac{{17}}{{13 + 17}} \times 2490$ .
If we solve them, we’ll get 1079 and 1411.
According to the question, the sum of two numbers is 2490.
Let the two numbers be a and b. Then we have:
$ \Rightarrow a + b = 2490 .....(i)$
Next, it is given in the question that 6.5% of one number is equal to 8.5% of other. From this we’ll get:
$
\Rightarrow \dfrac{{6.5}}{{100}} \times a = \dfrac{{8.5}}{{100}} \times b, \\
\Rightarrow 65a = 85b, \\
\Rightarrow 13a = 17b, \\
\Rightarrow a = \dfrac{{17}}{{13}}b \\
$
Putting the value of a in equation $(i)$, we’ll get:
\[
\Rightarrow \dfrac{{17}}{{13}}b + b = 2490, \\
\Rightarrow \dfrac{{30}}{{13}}b = 2490, \\
\Rightarrow b = \dfrac{{2490 \times 13}}{{30}}, \\
\Rightarrow b = 1079 \\
\]
Putting the value of b in equation $(i)$, we’ll get:
$
\Rightarrow a + 1079 = 2490, \\
\Rightarrow a = 2490 - 1079, \\
\Rightarrow a = 1411 \\
$
Thus the numbers are 1411 and 1079 respectively.
Note: Instead of assuming variables, we can directly solve the question using ratios. 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. Thus, we have to divide 2490 in the ratio 13:17.
So, our numbers will be $\dfrac{{13}}{{13 + 17}} \times 2490$ and $\dfrac{{17}}{{13 + 17}} \times 2490$ .
If we solve them, we’ll get 1079 and 1411.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

Why do noble gases have positive electron gain enthalpy class 11 chemistry CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers
