Your cart is empty.
Practice each question, then open the answer or worked solution.
Shikha has an order from a golf course designer to put palm trees through a (× 23) machine and then through a (× 33) machine. She thinks she can do the job with a single repeater machine. What single repeater machine should she use?
Ans: The work done by hook-up machine is equal to 2 x 2 x 2 x 3 x 3 x 3 = 216 = 63 So, she should use (x 63) single machine for the purpose.
Neha needs to stretch some sticks to 252 times their original lengths, but her (×25) machine is broken. Find a hook-up of two repeater machines that will do the same work as a (×252) machine. To get started, think about the hookup you could use to replace the (×25) machine.
Ans: Work done by single machine (x 252) = 25 x 25 = 625 or 5 x 5 x 5 x 5 or 52 x 52 Hence, (x 52) and (x 52) hook-up machine can replace the (x 25) machine.
Supply the missing information for each diagram.
(a)
(b)
(c)
(d)
Ans: When a piece of length 5 cm is inserted in a single machine, it produces a piece having the same length of 5 cm.
Hence, it is a (x 1) repeated machine.
Therefore, the value of ? = 1.
Ans: When a piece of length 3 cm is inserted in a single machine, it produces a piece having the length 15 cm.
Hence, it is a (x 5) repeated machine.
Therefore, the value of ? = 5.
Ans: When a piece of length 1.25 cm is inserted in a (x 4) repeated machine, it will produce a piece that is 1.25 x 4 = 10 cm in length.
Therefore, the value of ? = 10 cm
Ans: When a piece of length x cm is inserted in (x 4) and (x 3)
hooked machine, it will produce a piece that is 36 cm in
length.
Hence, $x \times 4 \times 3 = 36$
$\dfrac{{{\text{Output}}}}{{{\text{Input}}}} = 12$
$\dfrac{{36}}{{12}} = 3{\text{ cm}}$
If possible, find a hook-up of a prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.
(a)
(b)
(c)
(d)
Ans: Single machine work = 100
Hook-up machine of prime base number that do the same work down by x 100
= 22 x 52
= 4 × 25
= 100
Ans: x 99 = 32 x 111 hook-up machine.
Ans: x 37 machine cannot do the same work.
Ans: x 1111 = 101 x 11 hook-up machine.
Find two repeater machines that will do the same work as a (× 81) machine.
Ans: Two repeater machines that do the same work as (x 81) are (x 34) and (x 92).
Since, factor of 81 are 3 and 9.
Find a repeater machine that will do the same work as a $\left( { \times \dfrac{1}{8}} \right)$ machine.
Ans: The repeater machine that performs the same
amount of work: $\dfrac{1}{8}$ are $\dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2}$
Hence, $\dfrac{1}{8} = \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = {\left( {\dfrac{1}{2}} \right)^3}$
Thus, $\left( { \times \dfrac{1}{{{2^3}}}} \right)$ repeater machine can perform the same work as a $\left( { \times \dfrac{1}{8}} \right)$ machine.
Find three machines that can be replaced with hook-ups of (× 5) machines.
Ans: Since, 52 = 25, 53 = 125, 54 = 625
Hence, (x 52), (x 53) and (x 54) machines can replace (x 5) hook-up machines.
The left column of the chart lists the lengths of input pieces of ribbon. Stretching machines are listed across the top. The other entries are the outputs for sending the input ribbon from that row through the machine from that column. Copy and complete the chart.
Input Length | Machine | |||
× 2 | ||||
1 | 5 | |||
3 | 15 | |||
14 | 7 | |||
Ans: In the given table, the left column of the chart list is the length of the input piece of ribbon. Thus, the outputs for sending the input ribbon are given in the following table.
Input Length | Machine | |||
× 2 | × 10 | ×1 | ×5 | |
5 | 1 | 5 | 0.5 | 2.5 |
3 | 6 | 30 | 3 | 15 |
7 | 14 | 70 | 7 | 35 |
The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.
Input Length | Repeater Machine | ||
× 23 | |||
40 | 125 | ||
2 | 162 | ||
81 | |||
Ans: In the given table, the left column of the chart lists the length of input chains of gold. Thus, the output we get when we send the input chain from the row through the repeater machine are detailed in the following table.
Input Length | Repeater Machine | ||
×23 | × 34 | × 52 | |
13.3 | 40 | 405 | 125 |
2 | 16 | 162 | 50 |
1 | 8 | 81 | 25 |
Long back in ancient times, a farmer saved the life of a king’s daughter. The king decided to reward the farmer with whatever he wished. The farmer, who was a chess champion, made an unusual request:
“I would like you to place 1 rupee on the first square of my chessboard, 2 rupees on the second square, 4 on the third square, 8 on the fourth square, and so on, until you have covered all 64 squares.
Each square should have twice as many rupees as the previous square.” The king thought this to be too less and asked the farmer to think of some better reward, but the farmer didn’t agree. How much money has the farmer earned?
Hint: The following table may help you. What is the first square on which the king will place at least Rs 10 lakh?
Position of Square on chess board | Amount (in Rs) |
1st square | 1 |
2nd square | 2 |
3rd square | 4 |
Ans: A grid of dimensions 8 x 8 is provided
We find the sum of each row-
e.g. The sum of the 1st row = 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 =
255
The sum of the 2nd row= 28 + 29 + 210 + 211 + 212 + 213 + 214 +
215
= 28 (20 + 21 + 22 + 23 + 24 + 25 + 26 + 27)
= 28 x 255 = 256 x 255 = 65280
The sum of the 3rd row= 216 x 255 = 16711680