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Q.6.    Convert given per cent to decimal fraction and also to fraction in simplest forms:

(a) 25%
(b) 150%
(c) 20%
(d) 5%

(a) 25 %
\Rightarrow \frac{25}{100} =0.25 = \frac{1}{4}

(b) 150%
\Rightarrow \frac{150}{100} =1.5 = \frac{3}{2}

(c) 20%
\Rightarrow \frac{20}{100} =0.2 = \frac{1}{5}

(d) 5%
\Rightarrow \frac{5}{100} =0.05 = \frac{1}{20}

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Q.5.    Find the whole quantity if

(a) 5% of it is 600.
(b) 12% of it is Rs 1080.
(c) 40% of it is 500 km.
(d) 70% of it is 14 minutes.
(e) 8% of it is 40 litres.

(a) Let the whole quantity be X
Therefore, 5 % of X = 600
\\\Rightarrow \frac{5}{100}\times X=600\\ \Rightarrow X = \frac{600\time 100}{5}=12000
Thus the required whole quantity is 12000

(b) 12 % of X = Rs 1080
\\\Rightarrow \frac{12}{100}\times X=1080\\ \Rightarrow X = \frac{1080\time 100}{12}=9000

(c) 40 % of X = 500 km
\\\Rightarrow \frac{40}{100}\times X=500\\ \Rightarrow X = \frac{50000\time 100}{40}=1250\ km

(d) 70% of X = 14 minutes
\\\Rightarrow \frac{70}{100}\times X=14\ min\\ \Rightarrow X = \frac{1400\time 100}{70}=20\ min

(e) 8 % of X = 40 litre
\\\Rightarrow \frac{8}{100}\times X=40\ L\\ \Rightarrow X = \frac{4000}{8}=500\ L

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Q: 4
Find: (a) 15\% of 250
         (b) 1\% of 1 hour
         (c) 20\%  of Rs 2500
         (d) 75\% of 1 kg

Here per cent implies for (\% \rightarrow \frac{1}{100})

Therefore, 
(a) 15% of 250
15\times \frac{1}{100}\times 250 =\frac{75}{2}
= 37.5

(b) 1\% of 1 hour
 = 1 \% of 60 minutes
=\frac{1}{100}\times 60 =\frac{3}{5}\ min
=\frac{3}{5}\times 60 = 36\ sec

 

 (c) 20\%  of Rs 2500
 =\frac{20}{100}\times 2500 =Rs\ 500

(d) 75\% of 1 kg
We know that 1kg = 1000 gm, therefore, 
\frac{75}{100}\times 1000g=750g
=0.75 kg

 

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Q.11.    If Meena gives an interest of Rs 45 for one year at 9% rate p.a. What is the sum she has borrowed?
 

Given that,
Principal =?
Interest = Rs 45
Time = 1 year

Rate= 9% p.a

Therefore, 
Principal = \frac{100\times I}{R\times T}
                       = \frac{100\times 45}{9\times 1} = Rs\ 500

Hence she borrowed total Rs 500

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Q.10.    What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?

Given that,
Principal = Rs 56,000
Interest = Rs 280
Time = 2 year

Rate= ?

Therefore, 
Rate = \frac{100\times I}{P\times T}
             = \frac{100\times 280}{56,000\times 2} = 0.25\%

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Q.9.    Find the amount to be paid at the end of 3 years in this case:

          (b) Principal = Rs 7,500 at 5% p.a.


 

Given that,
Principal (PA)= Rs 7,500 at 5% p.a. (Rate of interest)
and T = 3 year
We know that,
Interest = \frac{P\times R\times T}{100}
Now, putting the values in the above equation, we get
\Rightarrow \frac{7,500\times 5\times 3}{100} = Rs\ 1125 

So, Amount = PA + PI = 7,500 + 1125 = Rs 8625

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Q.9.    Find the amount to be paid at the end of 3 years in this case:

           (a) Principal = Rs 1,200 at 12% p.a.

Given that,
Principal (PA)= Rs 1,200 at 12% p.a. (Rate of interest)
and T = 3 year
We know that,
Interest = \frac{P\times R\times T}{100}
Now, putting the values in the above equation, we get
\Rightarrow \frac{1200\times 12\times 3}{100} = Rs\ 432 

So, Amount = PA + PI = 1200 + 432 = Rs 1632

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Q.8.    Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?
 

Here we have,
CP of the book = Rs 275
Loss = 15%

We know that,
SP = CP (1-\frac{Loss}{100}) = 275(1-\frac{15}{100})
                                                 = 275\times (\frac{85}{100})
                                                  = Rs\ 233.75

Hence the required selling price is Rs 233.75 

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Q.7.(ii)    If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?

We have the weight of the carbon = 3g
Therefore, the weight of the chalk 
\Rightarrow \frac{3}{3}\times 25g = 25g

Hence the weight of the chalk is 25g

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Q.7.(i)     Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.
 

We have,
The ratio of calcium, carbon and oxygen in the chalk = 10 : 3: 12
Now, Sum of the ratio = 10 + 3 + 12 = 25

Therefore, the percentage of carbon in the chalk
\Rightarrow \frac{3}{25}\times 100 =12\%

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