Question

Read the statements below to complete the tally chart and find the difference between the switches that are the most and least in number.

(i) The total number of blue and black switches is 13.
(ii) There are 2 more black switches than green switches.
(iii) There are 3 more red switches than blue switches.

Red switches	?
Blue switches	?
Black switches	?
Green switches

• A. Red switches = , Blue switches = , Black switches = ; 4
• B. Red switches = , Blue switches = , Black switches = ; 3
• C. Red switches = , Blue switches = , Black switches = ; 4
• D. Red switches = , Blue switches = , Black switches = ; 5

Answer 1

The correct option is A Red switches = , Blue switches = , Black switches = ; 4

As per the given information, there are four different types of switches - red, blue, black, and green.
Number of green switches $=5$

There are 2 more black switches than the green ones.
Number of black switches $=5+2$
$=7$
The total number of blue and black switches is 13.

So, we can find the number of blue switches by subtracting the number of black switches from the total.
Number of blue switches $=13-7$
$=6$

There are 3 more red switches than blue switches.
Number of red switches $=6+3$
$=9$

So, the complete tally chart will be as shown below.

Red switches
Blue switches
Black switches
Green switches

As per the tally chart, red switches are the most in number and green switches are the least.
Difference between the most and least number of switches
$=9-5$
$=4$

Hence, Option C is correct.