Given:
10 boys clear a piece of land in 21 days.
To find:
The number of days it will take 7 boys to clear the same land at the same rate.
Solution:
We have,
10 boys clear a piece of land in 21 days.
Total work =
![10* 21](https://img.qammunity.org/2022/formulas/mathematics/high-school/yiq6qh1wy0ey7mqvuemdsxi942comxtwj2.png)
=
![210](https://img.qammunity.org/2022/formulas/mathematics/college/v01ny50e4gqkt8w20gej5pxw05yo8kp3fo.png)
Let 7 boys clear the same piece of land in x days.
Total work =
![7* x](https://img.qammunity.org/2022/formulas/mathematics/high-school/mo6mqihl8qnrxsibhsih5cbb1rjt4egjhi.png)
=
![7x](https://img.qammunity.org/2022/formulas/mathematics/high-school/3chxsh3kd2he5z2eox5xekr4e4d0zaxvog.png)
Now, the total work is same.
![7x=210](https://img.qammunity.org/2022/formulas/mathematics/high-school/w3ee8v4z0w013q3ktps3zj49oy6a2jq0h8.png)
Divide both sides by 7.
![x=(210)/(7)](https://img.qammunity.org/2022/formulas/mathematics/high-school/pyp8kkqdz4y3nt8diiswa2yneyzp1sduxb.png)
![x=30](https://img.qammunity.org/2022/formulas/mathematics/college/3dw0w0eptuted5s6jy4n5xab3cc5z9aawo.png)
Therefore, 7 boys clear the same piece of land in 30 days.