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Practice each question, then open the answer or worked solution.
The cost of 27 kg of iron is Rs 1,080, what will be the cost of 120 kg of iron of the same quality?
Ans: 27 kg iron costs = Rs 1080
1 kg iron cost=$\dfrac{1080}{27}$ =Rs. 40
120 kg iron will cost = 120 × 40=Rs. 4800
At a particular time, the length of the shadow of Qutub Minar whose height is 72 m is 80 m. What will be the height of an electric pole, the length of whose shadow at the same time is 1000 cm?
Ans: Length of Qutub Minar = 72m
At a particular time its shadow = 80m
Shadow of the electric pole has a length of = 1000cm=10m
Length of electric pole = $\dfrac{72}{80}$ $\times $ 100 = 9m
In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?
Ans:50 girls can have the food = 40 Days
1 girl can have the food = 50×40=2000 Days
Total Girls = 50+30 =80
80 girls can have = $\dfrac{2000}{80}$ =25 Days
The Campus and Welfare Committee of the school is planning to develop a blue shade for painting the entire school building. For this purpose various shades are tried by mixing containers of blue paint and white paint. In each of the following mixtures, decide which a lighter shade of blue is and also find the lightest blue shade among all of them.
If one container has one liter paint and the building requires 105 liters for painting, how many containers of each type is required to paint the building in the darkest blue shade?
Ans: (i) In mixture A
Ratio of blue and white = $\dfrac{3}{4}$
In mixture B
Ratio of blue and white= $\dfrac{3}{3}$=1
Clearly mixture A will have a lighter shade
(ii) In mixture C
Ratio of blue and white = $\dfrac{3}{3}$=1
In mixture D Ratio
on blue and white = $\dfrac{2}{5}$=0.4
Clearly mixture D will have a lighter shade.
(iii) In mixture E
Ratio of blue and white=$\dfrac{6}{1}$=6
In mixture F
Ratio of blue and white= $\dfrac{4}{2}$=2
Clearly mixture F will have a lighter shade.
(iv) In mixture G
Ratio of blue and white=$\dfrac{3}{3}$=1
In mixture H Ratio of blue and white=$\dfrac{4}{3}$=1.33
Clearly mixture G will have a lighter shade.
Posing a question:
Work with a partner to write at least five ratio statements about this quilt, which has white, blue, and purple squares?
How many squares of each color will be there in 12 such quilts?
Ans: Purple = 12, Blue = 20 and white = 16
Total squares = 12+20+16=48
Statement I Purple: Totala = 12:48=5:12
Statement II Blue: Total = 20:48=1:3
Statement III White: Total = 16:48=1:3
Statement IV Purple: Blue= 12:20=3:5
Statement V Purple: White= 12:16=3:4
A packet of sweets was distributed among 10 children and each of them received 4 sweets. If it is distributed among 8 children, how many sweets will each child get?
Ans: 10 children received = 4 sweets
1 child receives = 10×4=40
8 children receive =$\dfrac{40}{5}$ = 8 sweets
44 cows can graze a field in 9 days. How many less/more cows will graze the same field in 12 days?
Ans: 9 days take to graze the field by = 44 cows
1 day will take more cows to graze = 44×9
12 days will take fewer cows to graze = $\dfrac{44 \times 9}{12}$ = 33 cows
Decreased number of cows = 44-33=11
30 persons can reap a field in 17 days. How many more people should be engaged to reap the same field in 10 days?
Ans: 17 days need to reap the field by =30 persons
1 day need to reap the field by more man= 30×17=510
10 days need to reap filed by less men= $\dfrac{510}{10}$ = 51 men
Shabnam takes 20 minutes to reach her school if she goes at a speed of 6 km/h. If she wants to reach school in 24 minutes, what should be her speed?
Ans: 20 minutes time Shabnam takes to reach with the speed =6km/hr
1 minute time will take a speed = 6×20=120km/hr
24 minutes time will take with a speed = $\dfrac{120}{24}$ = 5km / hr
Ravi starts for his school at 8:20 a.m. on his bicycle. If he travels at a speed of 10km/h, then he reaches his school late by 8 minutes but on traveling at 16 km/h he reaches the school 10 minutes early. At what time does school start?
Ans: Let the total distance = x km
Time taken = t min
With speed of bicycle 10km/hr , then he reaches by 8 min
$\dfrac{x}{10}$ = t+ $\dfrac{8}{60}$ $\Rightarrow $ $\dfrac{x}{10}$ = t+ $\dfrac{2}{15}$…(1)
With speed 16km/hr then reaches his school 10 min early
$\dfrac{x}{16}$ = t- $\dfrac{10}{60}$ $\Rightarrow $ $\dfrac{x}{16}$ = t-$\dfrac{1}{6}$ …(2)
On subtracting (2) from (1)
$\dfrac{x}{10}$ - $\dfrac{x}{16}$ = $\dfrac{2}{15}$ + $\dfrac{1}{6}$
$\Rightarrow $ $\dfrac{8x-5x}{80}$ = $\dfrac{4+5}{30}$
$\Rightarrow $ $\dfrac{3x}{80}$ = $\dfrac{9}{30}$
$\Rightarrow $ x = $\dfrac{9\times 80}{30 \times 3}$
$\Rightarrow $ x =8
Now, put x=8 in eq. (i), we get
$\dfrac{8}{10}$ = t+ $\dfrac{8}{60}$
$\Rightarrow $ $\dfrac{8}{10}$ - $\dfrac{2}{15}$= t
$\Rightarrow $ $\dfrac{24-4}{30}$ = t
$\Rightarrow $ $\dfrac{20}{30}$ = t $\Rightarrow $ t=$\dfrac{2}{3}$