Question

Vijay weighed $65{\displaystyle \frac{1}{2}}\text{kg}$ . He gained $1{\displaystyle \frac{2}{5}}\text{kg}$ during the first week, $1{\displaystyle \frac{1}{4}}\text{kg}$ during the second week, but lost ${\displaystyle \frac{5}{16}}\text{kg}$ during the third week. What was his weight after the third week?

Answer 1

Hint: The data given in the question is that the weight of Vijay is increasing or decreasing week by week. If the weight is gained or increased, we have to add the gained weight. If the weight is decreased or lost, we have to subtract the gained weight.

Complete step-by-step answer:
The data given in the question are,
The weight of Vijay at initial stage is $65{\displaystyle \frac{1}{2}}\text{kg}$
During the first week, the weight gained by Vijay is $1{\displaystyle \frac{2}{5}}\text{kg}$
During the second week, the weight gained by Vijay is $1{\displaystyle \frac{1}{4}}\text{kg}$
During the third week, the weight lost by Vijay is ${\displaystyle \frac{5}{16}}\text{kg}$

To find the weight of Vijay during third week,
During third week, the weight of Vijay is,
 $\Rightarrow 65{\displaystyle \frac{1}{2}}+1{\displaystyle \frac{2}{5}}+1{\displaystyle \frac{1}{4}}-{\displaystyle \frac{5}{16}}$
 After converting the mixed fraction into the normal fraction we get,
 $$\Rightarrow {\displaystyle \frac{131}{2}}+{\displaystyle \frac{7}{5}}+{\displaystyle \frac{5}{4}}-{\displaystyle \frac{5}{16}}$$
By taking L.C.M we get,
The L.C.M of above equation is $80$
By solving we get,
 $\Rightarrow {\displaystyle \frac{5240+112+100-25}{80}}$
By adding the numerator, we get,
 $\Rightarrow {\displaystyle \frac{5452-25}{80}}$
By subtracting the numerator, we get,
 $\Rightarrow {\displaystyle \frac{5427}{80}}\text{kg}$
If we converting the above term into the mixed fraction we get,
 $\Rightarrow 67{\displaystyle \frac{67}{80}}\text{kg}$
 $\therefore$The weight of Vijay during the third week is $67{\displaystyle \frac{67}{80}}\text{kg}$ .
Hence, the weight of Vijay during the third week is $67{\displaystyle \frac{67}{80}}\text{kg}$ .

Note: We have to do subtraction for the lost weight. To gain weight we have to do addition. We can give the final answer as in mixed fraction or we can divide and give it as decimal values.