A water tank is filled from a tap. If the tap is open for 1 hour, 7/10 of the tank. Class 7

A water tank is filled from a tap. If the tap is open for 1 hour, 7/10 of the tank. Class 7

Question 1.

A water tank is filled from a tap. If the tap is open for 1 hour, [latex]\frac {7}{10}[/latex] of the tank 10 gets filled. How much of the tank is filled if the tap is open for: Class 7

(a) [latex]\frac {1}{3}[/latex] hour _________

Solution:

In [latex]\frac {1}{3}[/latex] hours, tank filled will be

= [latex]\frac {1}{3}[/latex] × [latex]\frac {7}{10}[/latex] = [latex]\frac{1 \times 7}{3 \times 10}[/latex] = [latex]\frac {7}{30}[/latex]

(b) [latex]\frac {2}{3}[/latex] hour _________

Solution:

In [latex]\frac {2}{3}[/latex] hours, tank filled will be

= [latex]\frac {2}{3}[/latex] × [latex]\frac {7}{10}[/latex] = [latex]\frac{2 \times 7}{30}[/latex] = [latex]\frac{2 \times 7}{2 \times 15}[/latex] = [latex]\frac {7}{15}[/latex]

(c) [latex]\frac {3}{4}[/latex] hour _________

Solution:

In [latex]\frac {3}{4}[/latex] hours, tank filled will be

= [latex]\frac {3}{4}[/latex] × [latex]\frac {7}{10}[/latex] = [latex]\frac{3 \times 7}{4 \times 10}[/latex] = [latex]\frac {21}{40}[/latex]

(d) [latex]\frac {7}{10}[/latex] hour _________

Solution:

In [latex]\frac {7}{10}[/latex] hours, tank filled will be

= [latex]\frac {7}{10}[/latex] × [latex]\frac {7}{10}[/latex] = [latex]\frac{7 \times 7}{10 \times 10}[/latex] = [latex]\frac {49}{100}[/latex]

(e) For the tank to be full, how long should the tap be running?

hours, tank filled will be

Solution:

For filling the full tank, tap should be open for [latex]\frac {10}{7}[/latex] hours, because

[latex]\frac {7}{10}[/latex] × [latex]\frac {10}{7}[/latex] = [latex]\frac{7 \times 10}{10 \times 7}[/latex] = [latex]\frac {70}{70}[/latex] = 1, i.e., for

[latex]\frac {7+3}{7}[/latex] = [latex]\frac {7}{7}[/latex] + [latex]\frac {3}{7}[/latex] = 1 +[latex]\frac {3}{7}[/latex] = 1[latex]\frac {3}{7}[/latex] hours.

Question 2.

The government has taken [latex]\frac {1}{6}[/latex] of Somu's land to build a road. What part of the land remains with Somu now? She gives half of the remaining part of the land to her daughter Krishna and [latex]\frac {1}{3}[/latex] of it to her son Bora. After giving them their shares, she keeps the remaining land for herself. Class 7

(a) What part of the original land did Krishna get?

(b) What part of the original land did Bora get?

(c) What part of the original land did Somu keep for herself?

Solution:

Part of land remain with Somu

= 1 - [latex]\frac {1}{6}[/latex] = [latex]\frac {6}{6}[/latex] - [latex]\frac {1}{6}[/latex] = [latex]\frac {5}{6}[/latex]

Part of land given to Krishna

= [latex]\frac {1}{2}[/latex] of [latex]\frac {5}{6}[/latex] = [latex]\frac {1}{2}[/latex] × [latex]\frac {5}{6}[/latex] = [latex]\frac{1 \times 5}{2 \times 6}[/latex] = [latex]\frac {5}{12}[/latex]

Part of land given to Bora

= [latex]\frac {1}{3}[/latex] of [latex]\frac {5}{6}[/latex] = [latex]\frac {1}{3}[/latex] × [latex]\frac {5}{6}[/latex] = [latex]\frac{1 \times 5}{3 \times 6}[/latex] = [latex]\frac {5}{18}[/latex]

(a) Krishna got [latex]\frac {5}{12}[/latex] part of the original land.

(b) Bora got [latex]\frac {5}{18}[/latex] part of the original land.

(c) Part of the land Somu kept for herself

= [latex]\frac {5}{6}[/latex] - [latex]\frac {5}{12}[/latex] - [latex]\frac {5}{18}[/latex]

= [latex]=\frac{5 \times 6}{6 \times 6}[/latex] - [latex]=\frac{5 \times 3}{12 \times 3}[/latex] - [latex]=\frac{5 \times 2}{18 \times 2}[/latex]

= [latex]\frac {30}{36}[/latex] - [latex]\frac {15}{36}[/latex] - [latex]\frac {10}{36}[/latex]

= [latex]\frac {30-15-10}{36}[/latex] = [latex]\frac {5}{36}[/latex]