Question

Solve.
(1) Suyash bought $2\frac{1}{2}$ kg of sugar and Ashish bought $3\frac{1}{2}$ kg. How much sugar did they buy altogether? If sugar costs 32 rupees per kg, how much did they spend on the sugar they bought?
(2) Aradhana grows potatoes in$\frac{2}{5}$part of her garden, greens in $\frac{1}{3}$ part and brinjals in the remaining part. On how much of her plot did she plant brinjals?
(3) Sandeep filled water in$\frac{4}{7}$ of an empty tank. After that, Ramakant filled $\frac{1}{4}$part more of the same tank. Then Umesh used $\frac{3}{14}$ part of the tank to water the garden. If the tank has a maximum capacity of 560 litres, how many litres of water will be left in the tank?

Answer 1

(1) The amount of sugar they bought altogether = $2\frac{1}{2}+3\frac{1}{2}$
$$\begin{gathered} =\frac{5}{2}+\frac{7}{2} \\ =\frac{5+7}{2} \\ =\frac{{\displaystyle 12}}{{\displaystyle 2}} \end{gathered}$$
= 6 kg
Now, cost of 1 kg of sugar = Rs 32
Therefore, the cost of 6 kg of sugar is = 6 × 32
= Rs 192
Hence, they spend Rs 192 on the sugar they bought.

(2) The part of the garden in which Aradhana grew brinjals is given by $1-\frac{2}{5}-\frac{1}{3}$

$$\begin{gathered} =\frac{1\times 15}{1\times 15}-\frac{2\times 3}{5\times 3}-\frac{1\times 5}{3\times 5} \\ =\frac{15}{15}-\frac{6}{15}-\frac{5}{15} \\ =\frac{15-6-5}{15} \\ =\frac{4}{15} \end{gathered}$$
Hence, Aradhana grew brinjals in $\frac{4}{15}$ part of her garden.
(3) The amount of water will be left in the tank is given by $\frac{4}{7}\left(560\right)+\frac{1}{4}\left(560\right)-\frac{3}{14}\left(560\right)$
$$\begin{gathered} =320+140-120 \\ =340l \end{gathered}$$
Hence, 340 l of water will be left in the tank.