Simplification- Aptitude Questions and Answers - in Hindi

 If the 8 digit number 5668X25Y is divisible by 48. Find the least value of X + Y ? यदि 8 अंकों की संख्या 5668X25Y , 48 से विभाजित होती है। तो X + Y का कम से कम मान होगा? A) 10 B) 8 C) 9 D) 7 Correct Answer : 10 Explanation :if 5668X25Y is divisible by 48 then it should be divisible by co-prime of 48. There, 3*16 =>3*2*8 =>3*2*2*4=48 where 2, 3, 4, 8 and 16 are co-prime numbers of 48. 5668X25Y divisible by 8 , that means last 3 digit, 25Y should be divisible by 8. So, Y should be 6 5668X256 to be divisible by 3, that means sum of digits 5+6+6+8+X+2+5+6 should be divisible by 3 So, 38+X is divisible by 3, that means X will be = 1 or 4 or 7 5668X256 divisible by 16,that means last four digits X256 should be divisible by 16 So, suppose X=1, then last four digits 1256 is not divisible by 16. suppose X=4, then last four digits 4256 is divisible by 16. suppose X=7, then last four digits 7256 is not divisible by 16. Hence the correct number is 56684256,which is divisible by 48. Therefore, least value of X+Y=4+6=10 A two digit number is such that the product of its digits is 12. When 36 is added to the number, its digits are reversed. Find the number ? एक दो अंको की संख्याओ के अंको का गुणनफल 12 है। यदि संख्या में 36 जोड़ा जाय तो उसके अंक उलट जाते हैं,संख्या ज्ञात कीजिये? A) 62 B) 54 C) 45 D) 26 Correct Answer : 26 Explanation :Let the digits of number x and y, with x being the tens digit that means the number would be 10x+y. as per question product of digits x*y = 12 ---------------eq1 When 36 is added to this number the digits inter change their places, so: 10x + y + 36 = 10y + x 9x + 36 = 9y x + 4 = y ---------------- eq2 Now subsitute eq2 into eq1: x*y = 12 x*(x + 4) = 12 x2 + 4x - 12 = 0 (x + 6)(x - 2) = 0 x = -6 or 2 ignore the -ve value then x=2 and y=6. Hence number is 26 (there 26+36=62, which is reversed of 26). While typing, Vipin is four times as fast as Harish and Harish is thrice as fast as Shailendra. Shailendra takes 156 minutes to type an article. How much time Vipin will take? टाइप करते समय विपिन हरीश से चार गुना तेज है और हरीश, शैलेंद्र से तीन गुना तेज है। यदि शैलेंद्र एक आर्टिकल को टाइप करने में 156 मिनिट लेता है तो विपिन को कितना समय लगेगा? A) 10 minutes B) 18 minutes C) 13 minutes D) 20 minutes Correct Answer : 13 minutes Explanation :as given, if time taken by Shailendra to do any work is X, then Harish would be do that in X/3 ,and Vipin would be do in X/12 Shailendra takes 156 minutes So X=156 minutes thus Vipin would take X/12 => 156/12 => 13 minutes If the digits of a two digit number are interchanged the newly formed number is more than the original number by 18 and sum of the digit is 8 then what was the original number? यदि दो अंको की एक संख्या के अंको को आपस में बदल दिया जाये तो इस प्रकार प्राप्‍त नयी संख्या मूल संख्या से 18 अधिक है और संख्या के अंको का योग 8 है, तो मूल संख्या क्या थी ? A) 53 B) 26 C) 35 D) 42 Correct Answer : 35 Explanation :Let the digits of number x and y, where x is the tens place, y is the ones place that means Number is: 10x + y As given the sum of the digits is 8. x + y = 8 -------------eq1 If the digits are reversed, the new number is 18 greater than the original number. 10y + x = 18 + 10x + y y - x = 2 y = 2 + x --------------eq2 Substitute value of eq2 in eq1 x + 2 + x = 8 2x = 6 x = 3 So, y = 2 + x = 2 + 3 = 5 Hence number is: 10x + y = 10*3 + 5 = 35 54 is divided into two parts, so that 10 times the first and 22 times the second are together equal to 780. Find the product of the two numbers? 54 को दो भागो में इस तरह विभाजित किया जाता है कि पहले भाग का 10 गुना और दूसरे भाग का 22 गुना का योग 780 के बराबर है। तो दोनों भागो का गुणनफल ज्ञात करे? A) 408 B) 562 C) 860 D) 680 Correct Answer : 680 Explanation :Let 54 is divided into two parts (54 - x) and x. As given, 10 (54 - x) + 22x = 780 12x = 240 x = 20 and (54 - x) = 34 thus product of the two numbers 20*34=>680 The sum of one half,one third and one fourth of a number exceeds the number by 12. The number is? यदि एक संख्या के आधे, एक तिहाई एवं एक चौथाई का कुल योग संख्या से 12 अधिक है, तो संख्या है ? A) 144 B) 154 C) 90 D) 174 Correct Answer : 144 Explanation :let number is x then according to question x/3+x/2+x/4 = x+12 (6x+4x+3x) / 12 = x+12 13x = 12(x+12) 13x = 12x+144 13x-12x = 144 hence number is x=144. What should come in place of the question mark (?) in the following question (1442 ÷ 48 × 18 ÷ 36) = √? निम्नलिखित प्रश्‍न में (?) केस्थान पर क्या आना चाहिए? (1442 ÷ 48 × 18 ÷ 36) = √? A) 23328 B) 36 C) 216 D) 46656 Correct Answer : 46656 Explanation :((144)2 ÷ 48 × 18 ÷ 36) => (144*144*18) / (48*36) => (144*144*18) / (48*36) =>216 =>√(216*216) =>√46656 Divide 935 into three parts in such a way that half of the first part, 1/3 of the second part and 1/6 of the third part are equal. Then the third part is? 935 को तीन भागों में इस प्रकार बांटिए कि पहले भाग का आधा दूसरे भाग का 1/3 और तीसरे भाग का 1/6 बराबर है । तीसरा भाग है? A) 170 B) 255 C) 510 D) 1510 Correct Answer : 510 Explanation :Let equal part be x and three parts are A ,B and C there A *1/2= B *1/3=C *1/6= x A = 2x, B = 3x, C =6x A : B : C = 2 : 3 : 6 Thus,first part = 2x ,second part = 3x and third part = 6x as sum total of all parts = 935 therefore 2x+3x+6x = 935 11x = 935 x = 935/11 = 85 hence third part = 6x =6*85=510 If (1 + (27/169))1/2=1+(x/13) , then x equal? यदि (1 + (27/169))1/2=1+(x/13) है , तो x बराबर है ? A) 3 B) 1 C) 27 D) 13 Correct Answer : 1 Explanation :(1 + (27/169))1/2=1+(x/13) =>(1 + (27/169))1/2=1+(x/13) =>(196/169)1/2=1+(x/13) =>14/13=1+(x/13) =>(14/13)-1=x/13 =>1/13=x/13 Hence x=1 If (2x + 3y) : (3x + 5y) = 18 : 29 then x : y is equal to? यदि (2x + 3y) : (3x + 5y) = 18 : 29 तो x : y बराबर है ­? A) 2:3 B) 3:4 C) 3:5 D) 1:5 Correct Answer : 3:4 Explanation :(2x + 3y) : (3x + 5y) = 18 : 29 58x + 87y = 54x + 90y 58x - 54x = 90y - 87y 4x = 3y Thus, x : y = 3 : 4 If the sum of two numbers is 18 and sum of their square is 164 then the smallest number is? यदि दो संख्याओं का योग 18 और उनके वर्ग का योग 164 है , तो इनमें छोटी संख्या है ­? A) 8 B) 6 C) 12 D) 10 Correct Answer : 8 Explanation :Let the digits of number x and y, then x+y = 18 --------------eq1 x2+y2 = 164 ------------eq2 Substitute value of x from eq1 to in eq2 x = (18-y) (18-y)2 + y2 = 164 324 - 36y + y2 + y2 =164 324 - 36y + 2y2 = 164 2y2 -36y + 160 =0 2(y2 -18y + 80)=0 (y-10)(y-8)=0 y = 8 or 10 from eq1, if y= 8, then x+y = x+8 = 18 x = 10 if y= 10, then x+y = x+10 = 18 x = 8 So the numbers are 8 and 10.and smallest number is 8 (7 + 7 + 7 / 7) / (5 + 5 + 5 / 5) = ? A) 1 B) 1 / 5 C) 15 / 11 D) 3 / 11 Correct Answer : 15 / 11 Explanation :(7 + 7 + 7 / 7) / (5 + 5 + 5 / 5) = (14 + 1) / (10 + 1) =15 / 11 It is required to change a rupee coin into 2 paise and 5 paise coins with the total number of coins equal to 26. Find the number of each type of coins? 26 रुपये को 2 पैसे और 5 पैसे के सिक्के में बदलना है। तो प्रत्येक प्रकार के सिक्कों की संख्या क्या हे? A) 10 and 16 B) 12 and 14 C) 10 and 20 D) 14 and 14 Correct Answer : 10 and 16 Explanation :Let x be the number of 5 paise coins, then (26 - x) will be the number of 2 paise coins. So, 5*x + 2*(26 - x)= 100 5x + 52 - 2x = 100 3x = 48 x = 16 Number of 5 paise coins = 16 Number of 2 paise coins = 26 - 16 = 10 Let A = (x + 1)/(x - 1) and B = (x - 1)/(x + 1). Determine the value of A - B ? यदि A = (x + 1)/(x - 1) और B = (x - 1)/(x + 1) है । तो A - B का मान ज्ञात करें? A) 0 B) x/(x2 -1) C) 4x/(x2 - 1) D) 1 Correct Answer : 4x/(x2 - 1) Explanation :A - B = (x + 1)/(x - 1) - (x - 1)/(x + 1) =(x + 1)2 - (x - 1)2 / (x2 - 12) =(x2 + 1 + 2x - x2 - 1 + 2x) / (x2 - 1) =4x / (x2 - 1) A factory has a woman worker on every 9 workers . The number of women workers is 125, then the total number of workers are? एक फैक्ट्री में प्रति 9 कामगारो में से एक महिला कामगार है। यदि महिला कामगारो की संख्या 125 से तो कामगारो की कुल संख्या क्या होगी? A) 1250 B) 1125 C) 1025 D) 1000 Correct Answer : 1125 Explanation :total number of workers = 125*9 =1125 A, B and C earn Rs 150 daily, while A and C earn Rs 94 rupees, B and C earn Rs 76. How much is C earns per day? A, B और C मिलकर 150 रुपये प्रतिदिन कमाते हैं जबकि A और C मिलकर 94 रुपए कमाते हैं, B और C मिलकर 76 रुपये कमाते हैं । C की प्रतिदिन की कमाई कितनी है? A) 56 B) 20 C) 34 D) 75 Correct Answer : 20 Explanation :As given, A+C=94 -----eq1 B+C=76 -----eq2 A+B+C=150-----eq3 from eq2 and eq3 , A+76 =150 A=74 now from eq1, 74+C=94 C=20