Number System - Study Mode

[#196] If $$frac{{51.84}}{{4.32}} = 12$$ xa0, then the value of $$frac{{0.005184}}{{0.432}}$$ xa0 is :
Correct Answer

(B) 0.012

Explanation

Solution: Given : $$eqalign{
& Leftrightarrow frac{{51.84}}{{4.32}} = 12 cr
& Leftrightarrow frac{{5184}}{{432}} = 12 cr
& herefore frac{{0.005184}}{{0.432}} cr
& = frac{{5.184}}{{432}} cr
& = frac{{5184}}{{432}} imes frac{1}{{1000}} cr
& = 12 imes frac{1}{{1000}} cr
& = 0.012 cr} $$

[#197] How many $$frac{1}{6}$$ of together make $${ ext{41}}frac{2}{3}$$ ?
Correct Answer

(C) 250

Explanation

Solution: $$frac{{41frac{2}{3}}}{{frac{1}{6}}} = frac{{125}}{3} imes frac{6}{1} = 250{ ext{ times}}$$

[#198] A girl was asked to multiply a number by $$frac{7}{8}$$, instead she divided the number by $$frac{7}{8}$$ and got the result 15 more than the correct result. The sum of the digits of the number was -
Correct Answer

(D) 11

Explanation

Solution: $$eqalign{
& { ext{Let the number be x}} cr
& { ext{According to question}} cr
& frac{x}{{7/8}} - frac{7}{8}x = 15 cr
& frac{8}{7}x - frac{7}{8}x = 15 cr
& frac{{64x - 49x}}{{56}} = 15 cr
& 15x = 15 imes 56 cr
& x = 56 cr
& { ext{Sum of digits }} cr
& = 5{ ext{ }} + { ext{ }}6 cr
& = 11 cr} $$

[#199] The sum of three consecutive natural numbers each divisible by 5, is 225. The largest among them is ?
Correct Answer

(D) 80

Explanation

Solution: $$eqalign{
& { ext{Let number are }}x,{ ext{ }}x + 5,{ ext{ }}x + 10 cr
& { ext{So, }}x{ ext{ + }}x + 5 + x + 10 = 225 cr
& 3x + 15 = 225 cr
& 3x = 210 cr
& x = 70 cr
& { ext{largest number is }}70 + 10 = 80 cr} $$

[#200] A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is:
Correct Answer

(A) 220030

Explanation

Solution: Divisor = 555 + 445 = 1000 Quotient = 2(555 - 445) = 220 Remainder = 30 As we know, Dividend = Divisor × Quotient + Remainder Dividend = 1000 × 220 + 30 Dividend = 220000 + 30 ∴ Dividend = 220030