Q: Solve this inequality 3b - 7 < 32?

The given 3b - 7 < 32 can be solved as 3b - 7 < 32 3b < 39 b < 13.

Q: Simplify and find '?' 48?+32? = 320

given 48 ? + 32 ? = 320 => 6 ? + 4 ? = 40 Now squaring on both sides => 36 x ? + 16 x ? + 48 x ? = 1600 => 100 x ? = 1600 => ? = 16

Question 1

Solve this inequality 3b - 7 < 32?

Accepted Answer

The given 3b - 7 < 32 can be solved as 3b - 7 < 32 3b < 39 b < 13.

Question 2

Simplify and find '?' 48?+32? = 320

Accepted Answer

given 48 ? + 32 ? = 320 => 6 ? + 4 ? = 40 Now squaring on both sides => 36 x ? + 16 x ? + 48 x ? = 1600 => 100 x ? = 1600 => ? = 16

Question 3

The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 8 : 9. Then what is the number of visitors on…

Accepted Answer

If number of visitors on 1st, 2nd, 3rd, 4th & 5th day are k, l, m, n & o respectively, then k + l + m + n = 58 x 4 = 232 ---- (i) & l + m + n + o = 60 x 4 = 240 ---- (ii) Subtracting (i) from (ii), we get o-k = 8 ---(iii) Given, k/o = 8/9 ----(iv) So from (iii) & (iv), we get a = 64, e = 72 Therefore, number of visitors on 5th day is 72.

Question 4

Twenty times a positive integer is less than its square by 96. What is the integer ?

Accepted Answer

Let the integer be x. Then, x2 - 20x = 96 (x + 4)(x - 24) = 0 x = 24

Question 5

In a slip test, K got the 15th rank and he was 44th from the bottom of the list of passed students. 4 students did not take up the slip test and 3 students were failed. What is the total strenght of the class ?

Accepted Answer

Total strength of the class is given by 15 + 44 + 4 + 3 - 1 = 65

Question 6

If 3x+7=x2+p=7x+5 , what is the value of P ?

Accepted Answer

3 x + 7 = 7 x + 5 = > 7 x - 3 x = 2 = > 4 x = 2 = > x = 2 Now, 3 x + 7 = x 2 + p = 3 2 + 7 = 1 4 + p = > p = 17 2

Question 7

An owner of a Dry fruits shop sold small packets of mixed nuts for Rs. 150 each and large packets for Rs. 250 each. One day he sold 5000 packets, for a total of Rs. 10.50 lakh. How many small packets were sold ?

Accepted Answer

Let 's' be the number of small packets and 'b' the number of large packets sold on that day. Therefore, s + b = 5000 ... eqn (1) Each small packet was sold for Rs.150. Therefore, 's' small packets would have fetched Rs.150s. Each large packets was sold for Rs.250. Therefore, 'b' large packets would have fetched Rs.250b. Total value of sale = 150s + 250b = Rs. 10.5 Lakhs (Given) Or 150s + 250b = 10,50,000 ... eqn (2) Multiplying equation (1) by 150, we get 150s + 150b = 7,50,000 ... eqn (3) Subtracting eqn (3) from eqn (2), we get 100b = 3,00,000 Or b = 3000 We know that s + b = 5000 So, s = 5000 - b = 5000 - 3000 = 2000. 2000 small packets were sold.

Question 8

Two numbers are such that the sum of twice the first number and thrice the second number is 36 and the sum of thrice the first number and twice the second number is 39. Find the difference between the numbers?

Accepted Answer

Let the required two numbers be a, b From the given data, 2a + 3b = 36 .....(1) 3a + 2b = 39 .....(2) Now, by solving 1 and 2 eqnts, we get 5a = 45 a = 9 ....(3) Put (3) in (1), we get 2(9) + 3b = 36 => 18 + 3b = 36 3b = 36 - 18 => b = 18/3 = 6 Required, difference between the numbers = a + b = 9 + 6 = 15.

Question 9

If a - b = 3, a2+b2=29 , find the value of ab.

Accepted Answer

2ab= a 2 + b 2 - a 2 - b 2 29-9=20 =>ab=10

Question 10

If x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y ?

Accepted Answer

x = y <=> 1 - q = 2q + 1 <=> 3q = 0 <=> q = 0.

Question 11

18800÷470÷20=?

Accepted Answer

Given Expression = 18800 470 ÷ 20 = 40 ÷ 20 = 2

Question 12

50.003% of 99.8÷49.988 = ?

Accepted Answer

50.003% of 99.8 ÷ 49.988 = ? ? ~= (50 x 100/100)/50 ? ~= (50 x 100)/(100 x 50) ? ~= 1

Question 13

If ab=45 and bc=1516 , then c2-a2c2+a2 is :

Accepted Answer

a b × b c = 4 5 × 15 16 = 3 4 = 16 - 9 16 + 9 = 7 25

Question 14

5 + 2 x 10/2 = ?

Accepted Answer

Using BODMAS Rule, First solve division, mutiplication and Addition So here 10/2 = 5 Then 2 x 5 = 10 Now, 5 + 10 = 15. Hence, 5 + 2 x 10/2 = 15.

Question 15

5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

Accepted Answer

Given, 5sinx + 12cosx ≥ -r ⇒ 13 5 13 sin x + 12 13 cos x ≥ - r cosx) ≥ -r 5 13 = cosA => sinA = 12 13 => 13(sinx cosA + sinA cosx) ≥ -r => 13(sin(x + A)) ≥ -r we know that , -1 ≤ sin (angle) ≤ 1 => 13sin (x + A) ≥ -13 ⇒ r m i n = 13

Question 16

A secret can be told to only 3 persons in 3 minutes. Each person in turn tells 3 other persons in the next 3 minutes and the processes continues accordingly. In 30 minutes how many persons can be told this secret in this way ?

Accepted Answer

Given a secret is told to 3 persons in 3 minutes. And if the process continues with each person saying 3 other persons, In 30 minutes => the rocess for 10 times because each person time is 3 minutes. Required number of persons = 3 + 3 2 + 3 3 + . . . . + 3 9 + 3 10 Now it forms a geometric progression, Sum to n terms is S = a r n - 1 r - 1 Here a = 3, r = 3 => 59048 x 3 /2 = 88572.

Question 17

A tailor has 37.5 metres of cloth and he has to make 8 pieces out of a metre of cloth. How many pieces can he make out of half of the cloth he has ?

Accepted Answer

Half of the cloth = 37.5/2 From 1 meter he will make 8 pieces => in 37.5/2 ---- ? 37.5/2 x 8 = 150.

Question 18

Simplify the following equation [K-L2-K+L2]4K = a/b

Accepted Answer

[ ( K - L ) 2 - K + L 2 ] 4 K = a b K 2 + L 2 - 2 K L - K 2 + L 2 + 2 K L 4 K = a b => - 4KL/4K = a/b => L = - a/b => bL = -a

Simplification Questions