Test: Word Problems - JEE MCQ

T = 30 + 25 (x – 3), 3 < x < 15
It is given 200 < T < 300
200 < 30 + 25 (x – 3) < 300
170 < 25(x - 3) < 270
170/25  (x - 3) < 270/25
6.8 + 3 < x < 10.8 + 3
9.8 < x < 13.8

Let x litres of 4% boric acid solution is required to be added
Then, total mixture = (x + 750)litres
This resulting mixture is to be  more than 5% but less than 8% boric acid
Total amount of acid = 750 of 10% + x of 4%
ATQ 
5/100(750 + x) < (750*10 + 4x)/100 < 8/100(750 + x)
3750 + 5x < 7500 + 4x ; 7500 + 4x < 6000 + 8x
x < 3750  ;   x > 375 
375 and 3750

Let x be the smaller of the two consecutive even positive integers .
Then the other integer is x+2.
Since both the integers are larger than 7,x > 7 ....(1)
Also the sum of the two integers is less than 28.
x + (x + 2) < 28
⇒ 2x + 2 < 28
⇒ 2x < 28 − 2
⇒ 2x < 26
=> x < 13…...(2)
From(1) and (2), we get
7 < x <13
Since x is an even number, x can take the values 8, 10 and 12.
Thus the required possible pairs are (8,10),(10,12) and (12,8).

Temperature is defined as the degree of hotness.
Temperature is measured using different scales in different regions.
we know that
 C = temperature in celcius.
F = temperature in Fahrenheit.
F= 9(C)/5 + 32
1) C = 30
F= 9(30)/5 + 32
F= 54 + 32 = 86F
2) C = 35
F= 9(35)/5 + 32
F= 63 + 32 = 95F
The range of temperatures in degree Fahrenheit is 86 F to 95 F.

Let the length of the shortest piece, The length of the second price is (x+6)cm. The length of the third piece is 3x cm, Total length of the three prieces must be ≤91cm.
xcm+(x+6)cm+3xcm≤91cm
=>5x+6≤91
Subtracting 6 from number 5 on both sides, 5x/5≤85/5
x≤17----(1)
Step 2:
Also third piece is at least 4 cm longer than the second piece. therefore
3x≥(x+6)+4
=>3x≥x+10
Subtracting x from both sides,
3x−x≥10
x≥5 -----(2)
Step 3:
From (1) and (2)
5≤x≤17

Your question is not complete it should be,
I: &600 fix and &50 per hourNow solving the question,Let the work is done in n hour as per given , So After n hour according to first scheme he will get an amount
= 600+50n After n hour according to second scheme he will get an amount,
=170nNow we are asked for values of n such that scheme
I give better wages so 600+50n >170n600>120nor n <5 .SO if the numbers of hour are less than 5 then he will get better wages by first scheme.

Profit = revenue - cost
But given profit > 0
therefore R(x) - C(x) >0
therefore 4x - 380 >0
therefore 4x > 380
therefore x>95  manufacturer must sell 96 items.

85≤MA/CA×100≤145
(85*12)/100≤MA/CA×100≤(145*12)/100
10.2≤MA≤17.4
range of mental age is[10.2,17.4].