Question

the least whole number when substracted from both the terms of the ratio to 6:7 gives a ratio less than 16:21 is?​

Answer 1

Answer:  The least whole number is 3.

Step-by-step explanation:  We are given to find the least whole number which when subtracted from both the terms of the ratio 6 : 7 gives the ratio less than 16 : 21.

Let n be the required whole number.

Then, according to the given information, we have

$\dfrac{6-n}{7-n}<\dfrac{16}{21}\\\\\\\Rightarrow 21(6-n)<16(7-n)\\\\\Rightarrow 126-21n<112-16n\\\\\Rightarrow -21n+16n<112-126\\\\\Rightarrow -5n<-14\\\\\Rightarrow 5n>14\\\\\Rightarrow n>\dfrac{14}{5}\\\\\Rightarrow n>2.8.$

Thus, the least whole number is 3.