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Syllabus

Q21. A steamer, going downstream in a river, covers the distance between two towns in 20 hours. Coming back upstream, it covers this distance in 25 hours. The speed of water is 4 km/h. Find the distance between the two towns.

[ Hint : First find the speed of the steamer in still water.]

Q22. Ranjana's mother gave her Rs.245 for buying New Year cards. If she got some 10-rupee cards, $\frac{2}{3}$ as many 5 rupee cards, and $\frac{1}{5}$ as many 15 rupee cards, how many of each kind did she buy ?

Q23. The enrolment in a school this year is 552. This is an increase of 15% over last year's enrolment. How many were enrolled last year?

Q24. A fruit vendor buys some oranges at the rate of Rs. 5 per orange. He also an equal number of bananas at the rate of Rs.2 per banana. He makes a 20% profit on oranges and a 15% profit on bananas. At the end of the day, all the fruit is sold out. His total profit is Rs.390. Find the number of oranges purchased.

Q. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The time taken by A to complete the remaining work is:

(a) 8 days

(b) 12 days

(c) 7 days

(d) 15 days

Solve this :Find x.

$1.\frac{2}{3}\mathrm{x}+\frac{1}{2}=\frac{3}{5}\mathrm{x}-\frac{5}{6}$

Q22. Ranjana's mother gave her Rs. 245 for buying New year cards. If she got some 10-rupee cards, $\frac{2}{3}$ as many 5 rupee cards, and $\frac{1}{5}$as many 15-rupee cards , how many of each kind did she buy .

Q. Solve the following equations.

15. $\frac{{\displaystyle \frac{x}{4}-\frac{3}{5}}}{{\displaystyle \frac{4}{3}-7x}}=-\frac{3}{20}$

4(2x+1)=3(x-1)+7

3(2p-1)=5-(3p-2)

5y-2[y-3(y-5)]=6

Please solve these equation fast

Answer.... 60/ 13

PLEASE solve this sum and give the answer with explanations. This sum is an absolute emergency.

Regards,

Soumili

$\frac{1}{x+1}+\frac{1}{x+2}=\frac{2}{x+10}$

Solve this :Solve the following systems of simultaneous linear equations by the substitution method.$1.\left(\mathrm{i}\right)\mathrm{x}+\mathrm{y}=14\left(\mathrm{ii}\right)\mathrm{s}-\mathrm{t}=3\phantom{\rule{0ex}{0ex}}\mathrm{x}-\mathrm{y}=4\frac{\mathrm{s}}{3}+\frac{\mathrm{t}}{2}=6\phantom{\rule{0ex}{0ex}}\left(\mathrm{iii}\right)2\mathrm{x}+3\mathrm{y}=9\left(\mathrm{iv}\right)3\mathrm{x}-5\mathrm{y}=4\phantom{\rule{0ex}{0ex}}3\mathrm{x}+4\mathrm{y}=59\mathrm{x}-2\mathrm{y}=7\phantom{\rule{0ex}{0ex}}$

Q.9. $3x+8y=\frac{11}{20}\phantom{\rule{0ex}{0ex}}2x+9y=\frac{11}{10}$

Solve this sum.

17. The sides (other than hypotenuse) of a right triangle are in the ratio 3:4. A rectangle is described on its hypotenuse,the hypotenuse being the longer side of the rectangle.The breadth of the rectangle is four-fifth of its length.Find the shortest side of the right triangle,if the perimeter of the rectangle is 180cm.

$[\mathrm{Hint}:\mathrm{Hypotenuse}=\sqrt{\mathrm{sum}\mathrm{of}\mathrm{sqaures}\mathrm{of}\mathrm{sides}}=\sqrt{{\left(3\mathrm{x}\right)}^{2}+(4\mathrm{x}{)}^{2}}=\sqrt{25{\mathrm{x}}^{2}}=5\mathrm{x}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle}=\frac{4}{5}\left(5\mathrm{x}\right)=4\mathrm{x}]$

x-5y-4=0