简化 - 例题解析

答案 - B

解释

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

答案 - A

解释

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

答案 - A

解释

Given exp. (a+b)2 -(a-b)2/ab ,  where a  = 598 , b = 479
= 4ab / ab = 4

答案 - B

解释

Given exp.  =  (a+b)2 +(a-b)2,  Where  a= 736, b= 278
(a2 +b2)
= 2(a2+b2)/(a2+b2) = 2

答案 - C

解释

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

答案 - A

解释

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

答案 - D

解释

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

答案 - D

解释

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 

答案 - B

解释

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

答案 - B

解释

Given exp.  2/3 *3/4 *4/5 * ...* 98/99 * 99/100= 2/100 = 1/50

答案 - A

解释

Given exp.= (1-1/2 ) (1-1/3)(1- 1/2)...(n-2)/ (n-1) * (n-1)/n = 1/n

答案 - A

解释

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.

答案 - B

解释

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

答案 - A

解释

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

答案 - A

解释

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.

答案 - B

解释

If the number  be x then, 
3/7 of 2/5 of x =  198 
⇒ 6x/35 = 198  
⇒ x = (198* 35/6 )  = (33*35) = 1155. 

答案 - A

解释

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.

答案 - A

解释

Let the number be x. then ,
52x-25x = 324 ⇒ 27x = 324 ⇒ x = 12 
∴  Required number = 12

答案 - B

解释

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.

答案 - A

解释

If x is the value of  VCR then,  the cost  of the  TV is  = 3x/2 
x+ 3x/2 = 35000 ⇒  5x = 70000 ⇒ x = 14000