Simplification - Study Mode

[#116] $${ ext{If }}left[ {4 - frac{5}{{1 + frac{1}{{3 + frac{1}{{2 + frac{1}{4}}}}}}}}
ight]$$ xa0xa0
part of a journey takes ten minutes, then to complete $$frac{3}{5}$$th of that journey, it will take = ?
Correct Answer

(C) 48 minutes

Explanation

Solution: $$eqalign{
& { ext{According to question,}} cr
& ,,,left[ {4 - frac{5}{{1 + frac{1}{{3 + frac{1}{{2 + frac{1}{4}}}}}}}}
ight] cr
& = 4 - frac{5}{{1 + frac{1}{{3 + frac{1}{{frac{9}{4}}}}}}} cr
& = 4 - frac{5}{{1 + frac{1}{{3 + frac{4}{9}}}}} cr
& = 4 - frac{5}{{1 + frac{1}{{frac{{31}}{9}}}}} cr
& = 4 - frac{5}{{1 + frac{9}{{31}}}} cr
& = 4 - frac{5}{{frac{{40}}{{31}}}} cr
& = 4 - frac{{5 imes 31}}{{40}} cr
& = 4 - frac{{31}}{8} cr
& = frac{1}{8} cr
& { ext{According to question}} cr
& frac{1}{8}{ ext{part = 10 minutes}} cr
& { ext{1 part = 10 minutes}} cr
& frac{3}{5}{ ext{ part = 80}} imes frac{3}{5} cr
& { ext{ = 48 minutes}} cr} $$

[#117] $$sqrt {frac{{4frac{1}{7} - 2frac{1}{4}}}{{3frac{1}{2} + 1frac{1}{7}}} div frac{1}{{2 + frac{1}{{2 + frac{1}{{5 - frac{1}{5}}}}}}}} $$ xa0 xa0 is equal to = ?
Correct Answer

(A) 1

Explanation

Solution: $$eqalign{
& { ext{Take first part }} cr
& frac{{4frac{1}{7} - 2frac{1}{4}}}{{3frac{1}{2} + 1frac{1}{7}}} cr
& = frac{{frac{{29}}{7} - frac{9}{4}}}{{frac{7}{2} + frac{8}{7}}} cr
& = frac{{frac{{116 - 63}}{{28}}}}{{frac{{49 + 16}}{{14}}}} cr
& = frac{{53}}{{28}} imes frac{{14}}{{65}} cr
& = frac{{53}}{{130}} cr
& { ext{The second part}} cr
& frac{1}{{2 + frac{1}{{2 + frac{1}{{5 - frac{1}{5}}}}}}} cr
& = frac{1}{{2 + frac{1}{{2 + frac{1}{{frac{{25 - 1}}{5}}}}}}} cr
& = frac{1}{{2 + frac{1}{{2 + frac{5}{{24}}}}}} cr
& = frac{1}{{2 + frac{1}{{frac{{53}}{{24}}}}}} cr
& = frac{1}{{2 + frac{{24}}{{53}}}} cr
& = frac{1}{{frac{{106 + 24}}{{53}}}} cr
& = frac{{53}}{{130}} cr
& { ext{According to question,}} cr
& ,,,,,,sqrt {frac{{53}}{{130}} div frac{{53}}{{130}}} cr
& = sqrt {frac{{53}}{{130}} imes frac{{130}}{{53}}} cr
& = sqrt 1 cr
& = 1 cr} $$

[#118] The cost of 5 pendants and 8 chains is Rs. 145785. What would be the cost of 15 pendants and 24 chains ?
Correct Answer

Rs. 325285

Explanation

Solution: $$eqalign{
& { ext{5P + 8C = 145785}} cr
& Rightarrow 3(5{ ext{P + 8C) = 3}} imes { ext{145785}} cr
& Rightarrow 15{ ext{P + 24C = 437355}} cr} $$

[#119] The simplification of $$left( {frac{{75983 imes 75983 - 45983 imes 45983}}{{30000}}}
ight)$$ xa0 xa0 xa0 yields the result = ?
Correct Answer

(D) 121966

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& ,,,,,frac{{{{left( {75983}
ight)}^2} - {{left( {45983}
ight)}^2}}}{{75983 - 45983}} cr
& = frac{{left( {75983 - 45983}
ight)left( {75983 + 45983}
ight)}}{{(75983 - 45983)}} cr
& = ,75983 + 45983 cr
& = 121966 cr} $$

[#120] The value of $$frac{5}{{1frac{7}{8}{ ext{of 1}}frac{1}{3}}} imes frac{{2frac{1}{{10}}}}{{3frac{1}{2}}}{ ext{ of 1}}frac{1}{4} = ?$$
Correct Answer

(A) $$1frac{1}{2}$$

Explanation

Solution: $$eqalign{
& { ext{According to the question}} cr
& frac{5}{{1frac{7}{8}{ ext{of 1}}frac{1}{3}}} imes frac{{2frac{1}{{10}}}}{{3frac{1}{2}}}{ ext{ of 1}}frac{1}{4} cr
& Rightarrow frac{5}{{frac{{15}}{8} imes { ext{ }}frac{4}{3}}} imes { ext{ }}frac{{21}}{{10}} imes frac{2}{7} imes frac{5}{4} cr
& Rightarrow 2 imes frac{3}{4} cr
& Rightarrow frac{3}{2} cr
& Rightarrow 1frac{1}{2} cr} $$