Number System - Study Mode
[#436] The sum of four consecutive even numbers is 748, The smallest among them is -
Correct Answer
(C) 184
Explanation
Solution: Let 'a' be the smallest even number According to question $$eqalign{
& (a) + (a + 2) + (a + 4) + (a + 6) = 748 cr
& 4a + 12 = 748 cr
& 4a = 736 cr
& a = 184 cr
& cr
& {x08f{Alternate :}} cr
& { ext{Middle term }} = frac{{748}}{4} = 187 cr
& underline {184} ,,,,underline {186} ,,,underline {188} ,,,underline {190} cr
& ,,,,,,,,,,,,,,,,,,mathop {187}limits^ downarrow cr
& { ext{Smallest number = 184}} cr} $$
[#437] $$1.overline {27} $$ xa0 in the form $$frac{{ ext{p}}}{{ ext{q}}}$$ is equal to :
Correct Answer
(C) $$frac{14}{11}$$
Explanation
Solution: $$eqalign{
& 1.overline {27} , = frac{{127 - 1}}{{99}}{ ext{ = }}frac{{126}}{{99}}{ ext{ = }}frac{{14}}{{11}} cr
& { ext{ }} herefore { ext{ }}frac{{ ext{p}}}{{ ext{q}}} = frac{{14}}{{11}} cr} $$
[#438] Of the three numbers, the sum of the first two is 55, sum of the second and third is 65, and sum of third with thrice of the first is 110. The third number is -
Correct Answer
(C) 35
Explanation
Solution: $$eqalign{
& { ext{Let the 3 numbers be }}x,y,& ,,z cr
& { ext{According to question}} cr
& x + y = 55 o y = 55 - x cr
& y + z = 65 o 55 - x + z = 65 cr
& z - x = 10.....(i) cr
& z + 3x = 110.....(ii) cr
& { ext{Solve (i)}},{ ext{and (ii)}} cr
& {x08f{z = 35,}} cr
& x = 25, cr
& y = 30 cr} $$
[#439] If the digit in the unit and the ten's places of a two digit number are interchanged, a new number is formed, which is grater then the original number by 63. Suppose the digit in the unit place of the original number the x. Then all the possible value of x are -
Correct Answer
(A) 7, 8, 9
Explanation
Solution: $$eqalign{
& { ext{Let the two digit number be }} cr
& 10y + x,,,,,{ ext{where}},,,y > x cr
& 10x + y - 10y - x = 63 cr
& 9x - 9y = 63 cr
& x - y = 7 cr
& {x08f{x = 7,8,9}}{ ext{ and}} cr
& y = 0,1,2 cr} $$
[#440] A, B, C and D purchase a gift worth Rs. 60. A pays $$frac{{1}}{{2}}$$ of what others are paying. B pays $$frac{{1}}{{3}}$$ of what others are paying and C pays $$frac{{1}}{{4}}$$ of what others are paying. What is the amount paid by D ?
Correct Answer
(A) 13
Explanation
Solution: A + B + C + D = 60 -----------> (1) Now According to Question, A = $$frac{1}{2}$$ (B + C + D) 2A = B + C + D Put the value of B + C + D in Equation 1 A + 2A = 60 3A = 60 A = 20 Now again according to Question B = $$frac{1}{3}$$ (A + C + D) A + C + D = 3B By Putting the Value of A + C + D in Equation 1 we get, B + 3B = 60 4B = 60 B = 15 Now again according to Question C = $$frac{1}{4}$$ (A + B + D) A + B + D = 4C By Putting the Value of A + B + D in equation 1 We get C + 4C = 60 5C = 60 C = 12 Since A + B + C + D = 60 20 + 15 + 12 + D = 60 D = 60 - 47 = 13 Amount of D = Rs. 13