Question

three fifth of work is done on the first day. On the second day three quarters of the remainder is completed,if on the third day seven eighth of what remained is done,what fraction of work still remains to be done?​

Answer 1

Let's say the total work to be done is represented by 1.

On the first day, three-fifths of the work is completed. Therefore, the remaining work to be done is 1 - 3/5 = 2/5.

On the second day, three-quarters of the remainder is completed. The remainder after the first day's work is 2/5. So, the work completed on the second day is 3/4 x 2/5 = 3/10. The remaining work to be done is 2/5 - 3/10 = 1/5.

On the third day, seven-eighths of what remained is done. The remaining work to be done after the second day's work is 1/5. So, the work completed on the third day is 7/8 x 1/5 = 7/40.

Therefore, the fraction of work still remaining to be done is 1/5 - 7/40 = 8/40 - 7/40 = 1/40.

Answer 2

Let's assume that the total work is represented by 1.

On the first day, three-fifths of the work is done, so the remaining fraction of work is 1 - 3/5 = 2/5.

On the second day, three-quarters of the remainder is completed. The remainder after the first day is 2/5, so three-quarters of 2/5 is (3/4) x (2/5) = 6/20 = 3/10. Therefore, the amount of work completed after the second day is 3/5 + 3/10 = 9/10.

On the third day, seven-eighths of what remained is done. The remaining fraction of work after the second day is 1 - 9/10 = 1/10. Therefore, seven-eighths of 1/10 is 7/80.

Thus, the total amount of work completed after three days is 9/10 + 7/80 = 73/80.

Therefore, the fraction of work still remaining to be done is 1 - 73/80 = 7/80.

So, 7/80 of the work still remains to be done.