Vijay weighed 6512kg- He gained 125kg during the first week- 114kg during the second week- but lost 516kg during the third week- What was his weight after the third week-

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Byju's Answer

Standard VI

Mathematics

Unitary Method

Vijay weighed...

Question

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

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Solution

Step 1: Convert the given statement into a mathematical equation
The weight gain should be added to his original weight and the weight loss should be subtracted from it.
So,
Final weight = $65 \frac{1}{2} + 1 \frac{2}{5} + 1 \frac{1}{4} - \frac{5}{16}$

= $\frac{65 \times 2 + 1}{2} + \frac{1 \times 5 + 2}{5} + \frac{1 \times 4 + 1}{4} - \frac{5}{16}$

= $\frac{130 + 1}{2} + \frac{5 + 2}{5} + \frac{4 + 1}{4} - \frac{5}{16}$

= $\frac{131}{2} + \frac{7}{5} + \frac{5}{4} - \frac{5}{16}$

Step 2: Convert the fractions into like fraction and find the final weight of Vijay

$\frac{131}{2} + \frac{7}{5} + \frac{5}{4} - \frac{5}{16}$

= $\frac{131 \times 40 + 7 \times 16 + 5 \times 20 - 5 \times 5}{80}$

= $\frac{5240 + 112 + 100 - 25}{80}$

= $\frac{5427}{80}$ kg

Hence, Vijay's weight after the third week is $\frac{5427}{80}$ or $67 \frac{67}{80}$ kg

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