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11). A garrison is provided with ration for 72 soldiers to last for 54 days. Find how long would the same amount of food last for 90 soldiers, if the individual ration is reduced by 10%?
Let the required number of days be x. | ||||

12). 3 men can do a piece of work in 18 days. 6 boys can also do the same work in 18 days. In how many days, 4 men and 4 boys together will finish the work?
3 men = 6 boys = 1 man = 2 boys Therefore, 4 man + r boys = 4 mean + 2 men = 6 men Therefore, 3 men can do a work in 18 days. Therefore, 1 man can do a work in 18 X 3 days. Therefore, 6 men can do the work in \( \Large \frac{18 \times 3}{6} \) days Therefore, Required number of days = \( \Large \frac{2000 \times 20}{25} \) = 9 days | ||||

13). 10 men and 8 women can together complete a work in 5 days. Work done by a woman is equal to the half of the work done by a man. In how many days, will 4 men and 6 women complete that work?
1 man = 2 women 10 men + 8 women = 20 women + 8 women = 28 women 4 men + 6 women = 8 women + 6 women = 14 women Because, 28 women do the work in 5 days. Therefore, 1 woman can do the same work in days. Therefore, 14 women will do the same work in \( \Large 28 \times 5 \) days Therefore, Required number of days = \( \Large \left(\frac{28 \times 5}{14}\right) = 2 \times 5 \) = 10 | ||||

14). If 12 men or 18 women can do a piece of work in 14 days, then how long will 8 men and 16 women take to finish the work?
12 men = 18 women = 1 man = \( \Large \frac{18}{12} \) women = \( \Large \frac{3}{2} \) women Therefore, 8men = \( \Large \frac{3}{2} \times 8 \) = 12 women Therefore, 8men + 16 women = 12 women + 16 women = 28 women Therefore, 18 women can do the work in 14 days Therefore, 1 woman can do the same work in \( \Large 14 \times 8 \) days. Therefore, 28 women can do the same work in \( \Large \frac{14 \times 18}{28} \) days. Therefore, Required number of days = \( \Large \frac{14 \times 18}{28} \) = 9 days | ||||

15). If cost of 12 pens is Rs.84, then what is the cost of 10 such pens?
Cost of 12 pens = Rs.84 Therefore, Cost of 1 pen = Rs. \( \Large \frac{84}{12} \) Cost of 10 pens = \( \Large \frac{84}{12} \times 10 \) = \( \Large 7 \times 10 \) = Rs.70 | ||||

16). If 16 dozens bananas cost Rs.360, then how many bananas can be bought in Rs.60?
Let the required number of bananas be x. 16 dozens bananas = \( \Large 16 \times 12 \) = 192 bananas Less bananas, Less cost (Direct proportion) 360 : 60 :: 192 : x x = \( \Large \frac{60 \times 192}{360} \) = 32 bananas | ||||

17). If price of m articles is Rs.n, then what is the price of 5 articles?
Price of m articles = Rs.n Therefore, Price of 1 article = Rs. \( \Large \frac{n}{m} \) Therefore, Price of 5 articles = Rs. \( \Large \frac{5n}{m} \) | ||||

18). Magaulal, a worker, makes an article in every \( \Large \frac{2}{3} \) h. If he works for \( \Large 7\frac{1}{2} \)h, then how many articles will he make?
In \( \Large \frac{2}{3} \) h, 1 article is made. Therefore, In 1h, \( \Large \frac{3}{2} \) articles are made. Therefore, In \( \Large 7\frac{1}{2} \)=\( \Large \frac{15}{2} \)h. = \( \Large \frac{3}{2} \times \frac{15}{2}=\frac{45}{4} \) articles are made. Theerefore, Required articles = \( \Large \frac{45}{4}=11\frac{1}{4} \). | ||||

19). Shantanu completes \( \Large \frac{5}{8} \) of a Job in 20 days. At this rate, how many more days will he take to finish the job?
Let the required number of days be x. Remaining work = \( \Large 1-\frac{5}{8}=\frac{3}{8} \) Less work, Less days (Direct proportion) \( \Large \frac{5}{8}:\frac{3}{8}\ ::\ 20:x \) => \( \Large x = \frac{3}{8} \times 20 \times \frac{8}{5} \) Therefore, x = 12 days | ||||

20). 20 men can build 56 m long wall in 16 days. What length of a similar wall can be built by 70 men in 3 days?
Let the required length be x m. More men, More length (Direct proportion) Less days, Less length (Direct proportion) Men 20 : 70 :: 56 : x Days 6 : 3 Therefore, \( \Large \left(20 \times 6 \times x\right) = \left(70 \times 3 \times 56\right) \) \( \Large x = \frac{70 \times 3 \times 56}{20 \times 6} = 98\ m \) |