Number System - Study Mode

[#76] Each member of a club contributes as much rupees and as much paise as the number of members of the club. If the total contribution is Rs. 2525, then the number of members of the club is :
Correct Answer

(D) 50

Explanation

Solution: Let the total member be x x members contribution is Rs. x And each member also contributes x paise So, total rupees is x member Rs. x = Rs. x 2 x member Rs. x paise = $$frac{x.x}{100}$$ Total rupees is $${x^2} + frac{{{x^2}}}{{100}} = 2525$$ 101x 2 = 2525 × 100 101x 2 = 101 × 25 × 100 x = 50

[#77] The sum of the cubes of two numbers in the ratio 3 : 4 is 5824. The sum of the numbers is :
Correct Answer

(B) 28

Explanation

Solution: Let numbers are = 3x, 4x (3x) 3 + (4x) 3 = 5824 27x 3 + 64x 3 = 5824 91x 3 = 5824 x 3 = $$frac{5824}{91}$$ x 3 = 64 x = 4 So, numbers are 3x = 3 × 4 = 12 4x = 4 × 4 = 16 Sum = 12 + 16 = 28

[#78] The value of $$left( {0.34overline {67} + 0.13overline {33} }
ight)$$ xa0 is :
Correct Answer

(B) $$0.48overline {01} $$

Explanation

Solution: 0.34676767 ..... + 0.13333333 ..... = 0.480101 ..... = $$0.48overline {01} $$

[#79] Arrange the following fraction in decreasing order : $$frac{3}{5},$$ $$frac{7}{9}$$ $$,frac{{11}}{{13}}$$
Correct Answer

(C) $$frac{{11}}{{13}},frac{7}{9},frac{3}{5}$$

Explanation

Solution: $$frac{3}{5},frac{7}{9},frac{{11}}{{13}}$$ $$eqalign{
& frac{3}{5} = 0.60, cr
& frac{7}{9} = 0.7, cr
& frac{{11}}{{13}} = 0.8 cr
& frac{{11}}{{13}}{ ext{ > }}frac{7}{9} > frac{3}{5} cr} $$

[#80] The greatest number will divide 3026 and 5053 leaving remainders 11 and 13 respectively?
Correct Answer

(A) 15

Explanation

Solution: Required Number can be given by:
HCF of (3026 - 11) and (5053 - 13) HCF of 3015 and 5040 = 15 To find HCF, we break the given numbers in their prime Factors 3015 = 3 × 3 × 5 × 67 5040 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 We take common multiples in these two given numbers to get required HCF And Common multiples are: 3 × 5 So, Required HCF = 15