Problems On Numbers - Study Mode

[#96] Find the whole number which when increased by 20 is equal to 69 times the reciprocal of the number.
Correct Answer

(B) 3

Explanation

Solution: Let the required number be x Then, $$eqalign{
& Leftrightarrow x + 20 = frac{{69}}{x} cr
& Leftrightarrow {x^2} + 20x - 69 = 0 cr
& Leftrightarrow {x^2} + 23x - 3x - 69 = 0 cr
& Leftrightarrow xleft( {x + 23}
ight) - 3left( {x + 23}
ight) = 0 cr
& Leftrightarrow left( {x + 23}
ight)left( {x - 3}
ight) = 0 cr
& Leftrightarrow x = 3,,,,,,,,,left[ {x08ecause x
e - 23}
ight] cr} $$

[#97] The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
Correct Answer

(C) 400

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{number}},{ ext{be}},x,{ ext{and}},y cr
& { ext{Then}},,xy = 9375,{ ext{and}},frac{x}{y} = 15 cr
& frac{{xy}}{{left( {x/y}
ight)}} = frac{{9375}}{{15}} cr
& Rightarrow {y^2} = 625 cr
& Rightarrow y = 25 cr
& Rightarrow x = 15y = left( {15 imes 25}
ight) = 375 cr
& herefore { ext{Sum}},{ ext{of}},{ ext{the}},{ ext{number}} cr
& = x + y = 375 + 25 = 400 cr} $$

[#98] The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
Correct Answer

(B) 23

Explanation

Solution: Let the numbers be x and y Then, x y = 120 and x 2 + y 2 = 289 ∴ ( x + y ) 2 = x 2 + y 2 + 2 x y = 289 + (2 x 120) = 529 ∴ x + y = $$sqrt {529} $$xa0 = 23

[#99] A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
Correct Answer

(B) 253

Explanation

Solution: Let the middle digit be x Then, 2 x = 10 or x = 5. So, the number is either 253 or 352 Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit. Hence, required number = 253

[#100] The sum of two number is 25 and their difference is 13. Find their product.
Correct Answer

(B) 114

Explanation

Solution: Let the numbers be x and y Then, x + y = 25 and x - y = 13 4 x y = ( x + y ) 2 - ( x - y ) 2 = (25) 2 - (13) 2 = (625 - 169) = 456 ∴ x y = 114