Question

The sum of three numbers is 212. If t ratio of the first to the second is 13:16 a that of the second to the third is 2:3, t. find the numbers. ​

Answer 1

Answer:

We are given that there are any three numbers, say x, y and z, and their sum is 212 i.e., x + y + z = 212.

Now, we are told that the ratio of first and second number is 13:16.

We can write this in terms of an equation as: xy=1316

From this, we can write x=1316y equation (1)

Now, the ratio of the second and the third equation is 2:3

We can write this in an equation as: yz=23

From this, we can say thatz=32y equation (2)

Substituting these values of x and z in the sum x + y + z = 212, we get

⇒1316y+y+32y=212⇒13y+16y+24y16=212⇒5316y=212⇒y=212×1653=64

Now, we get y = 64. Substituting it in equation (1), we get

⇒x=1316y⇒x=1316×64=13×4=52

⇒x=52

Now, substituting y = 64 in equation (2), we get

⇒z=32y⇒z=32×64=3×32=96⇒z=96

Therefore, the numbers are x = 52, y = 64 and z = 96.

Note: In this question, be careful while converting the ratios in terms of the numbers x, y and z and then also with how to put their individual values in the sum of the three numbers. You can also verify that if the obtained values of x, y and z have their sum equal to 212 or not i.e., 52+64+96 = 212.

Step-by-step explanation: