The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.
Last updated date: 27th Mar 2023
•
Total views: 308.4k
•
Views today: 6.94k
Answer
308.4k+ 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
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

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

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
