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Simplification - Solved Examples
Answer - B
Explanation
Given exp. =2- [3-{6-(5-4+3)}] [ Removing viranaculam] = 2 - [3-{6-(5-4+3)}] [ Removing ( )] = 2-[ 3- {6-4}] [ Removing {}] = 2-[3-2] [ Removing [ ]] =2-1 = 1
Answer - A
Explanation
Given exp . = 4.8 *1.8 / 3.6+ 0.6-1/5 (Removing of () ) = 4.8 * 1.8 * 1/ 3.6+ 0.6 -1/5 ( Removing /) = 2.4 +0.6- 0.2 (Removing *) = 3- 0.2 = 2.8
Answer - A
Explanation
Given exp. (a+b)2 -(a-b)2/ab , where a = 598 , b = 479 = 4ab / ab = 4
Answer - B
Explanation
Given exp. = (a+b)2 +(a-b)2, Where a= 736, b= 278 (a2 +b2) = 2(a2+b2)/(a2+b2) = 2
Q 5 - (47*47*47+35*35*35+ 26*26*26 -47*35*78)/(47*47+35*35+26*26- 47*35- 35*26-47*26) = ?
Answer - C
Explanation
Given Exp. a3+b3+c3-3abc, where a =47 , b= 35, c= 26 a2+ b2+c2- ab-bc -ca =(a+b+c) =(47+35+26)= 108
Answer - A
Explanation
Putting (a-b) =x, (b-c) =y and (c-a) = z ,then we find x+y+z = 0 ∴ x3 +y3 + z3 = 3xyz ∴ x3 +y3+ z3 / 6xyz = 3xyz/6xyz = 1/2
Answer - D
Explanation
We have (a+b+c)2 = (a2+b2+c2)+ 2(ab+bc+ca) ⇒ (13)2 = 69+ 2(ab+bc+ca ) ⇒ 2(ab+bc+ca) = (169-69) = 100 ⇒ (ab+bc+ca) = 50
Q 8 - We have a/b = 2/3, then what would be the value the 3a+5b/ 3a-5b =?
Answer - D
Explanation
Given exp. 3a+5b/ 3a-5b = 3(a/b)+5 /3(a/b)-5 = (3*2/3+2)/ ( 3 *2/3-5) = 2+2/2-5 = 4/-3 = -4/3
Q 9 - What should be the value of a,b,c if the we have positive integers of a, b and c such that the value of a2+b2 =45 and b2+c2 = 40.
Answer - B
Explanation
a2+b2 = 45 and b2+c2 =40 On subtracting ,we get a2-c2 =5 ⇒ (a+c) (a-c) = 5 ⇒ a+c= 5 and a-c = 1 ⇒ a = 3, c = 2 9+ b2 = 45 ⇒ b2 = 36 ⇒ b =6 ∴ a=3, b= 6 and c = 2
Answer - B
Explanation
Given exp. 2/3 *3/4 *4/5 * ...* 98/99 * 99/100= 2/100 = 1/50
Answer - A
Explanation
Given exp.= (1-1/2 ) (1-1/3)(1- 1/2)...(n-2)/ (n-1) * (n-1)/n = 1/n
Answer - A
Explanation
Given exp. = 1/5 + (999 + 494/495) * 99 = 1/5 + 999* 99 + 494/495 *99 = 1/5 +(1000-1) * 99 + 494/5 = 999000 -99+ 495/5 = 99000-99 +99 = 999000.
Answer - B
Explanation
x + 1/{ 1+ 1/(3+1/4 )} = 2 ⇒ x+ 1/ { 1+ 1/ (13/4) }=2 ⇒ x+ 1/ (1+ 4/13) = 2 = x + 1/( 17/13) = 2 ⇒ x+ 17/13 = 2 ⇒ x= (2-13/17) = x = 34-13/ 17 = 21/17
Answer - A
Explanation
1 / (1 + (2/3)/(1+ 2/3 + (8/9)/(1- 2/3))) = 1 / (1 + (2/3)/(1+ 2/3 + (8/9)/(1/3))) = 1 / (1 + (2/3)/(1+ 2/3 + (8/9)/3/1)) = 1 / (1 + (2/3)/(1+ 2/3 + 8/3)) = 1 / (1 + (2/3)/(13/3)) = 1 / (1 + 2/3 * 3/13) = 1 / (1 + 2/13) = 1 / (15/13) = 13/15
Q 15 - Find the value of 3/7 of the estate if the value of 4/5 of this estate is 16800.
Answer - A
Explanation
If we assume x Rs. is the estate value. Then, 4/5 *x = 16800 ⇒ x= (16800* 5/4) = 21000 ∴ 3/7 of the estate = Rs. (3/7 *21000) = Rs. 9000.
Answer - B
Explanation
If the number be x then, 3/7 of 2/5 of x = 198 ⇒ 6x/35 = 198 ⇒ x = (198* 35/6 ) = (33*35) = 1155.
Q 17 - Divide the amount 312 in such a way that 100 boys gets Rs. 3.60 each and each girl gets Rs. 2.40. How many girls are there?
Answer - A
Explanation
If x is the quantity of girls then, the quantity of boys = (100-x) ∴ 2.40 *x + 3.60 *(100-x) = 312 ⇒ 240/100 *x + {360*(100-x)/100} = 312 ⇒ 240x + 36000 - 360 x = 31200 ⇒ 120x = (36000- 31200 ) = 4800 ⇒ x = 4800/120 = 40 ⇒ quantity of girls = 40.
Q 18 - A boy wants to multiply a number by 25 but by mistake he multiplied it by 52 and he got the result which was 324 more in the comparisons of correct answer. Find the number?
Answer - A
Explanation
Let the number be x. then , 52x-25x = 324 ⇒ 27x = 324 ⇒ x = 12 ∴ Required number = 12
Q 19 - A cab start from his center with full capacity. Cab stops on stoppage A where 1/3 of the passanger shift down the cab and new 30 passenger entered in cab, in the next attempt cab stop on C Stoppage where 1/4 of the passengers shift down the cab and 12 new passenger entered in the cab and last stoppage which was C all the 84 passengers shifted down. Find how much passengers can board at a time?
Answer - B
Explanation
If x passenger can board / sit in a cab at the same time. Number of passanger between the stations from A to B = (x-x/3 +30) = (2x/3+ 30) Number of passanger between the stations from B to C = (2x/3+30)- 1/4 (2x/3+30)+12 = 3/4 (2x/30)+12 = x/2 +45/2+12 ∴ x/2+ 45/2+12= 84 ⇒ x+ 45+24 = 168 ⇒ x = (168-69)= 99 So, we can say 99 passengers can board at a time.
Q 20 - Total cost of a TV and VCR is Rs. 35000 . If the cost of tv is 3/2 times more in the comparisons of VCR. In that case what should be the value of VCR?
Answer - A
Explanation
If x is the value of VCR then, the cost of the TV is = 3x/2 x+ 3x/2 = 35000 ⇒ 5x = 70000 ⇒ x = 14000
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