Mix Test - 5

The nature numbers from \(102\) to \(112\) are:

\(103,104,105,106,107,108,109,110,111\)

Total number of natural number \(=9\)

Hence, the correct option is (A).

Given,

Weight of wheat \(=3 \frac{3}{4} kg =\frac{15}{4} kg\)

Weight of rice \(=2 \frac{1}{2} kg =\frac{5}{2} kg\)

So, the total weight of wheat and rice \(=\frac{15}{4}+\frac{5}{2}\)

\(=\frac{(15+5 \times 2)}{4}\)

\(=\frac{(15+10)}{4}\)

\(=\frac{25}{4} kg\)

\(=6 \frac{1}{4} kg\)

Hence, the correct option is (A).

Factor of \(36=2 \times 2 \times 3 \times 3\)

Factor of \(144=2 \times2 \times 2 \times 2 \times 3 \times 3\)

Taking common factor, we get 

HCF \(=2 \times 2 \times 3 \times 3=36\)

Hence, the correct option is (A).

\(-100\) is not a natural number.

Natural numbers are \(1,2,3,4, \ldots\). This set does not include negative numbers, \(0\) or decimal fractions. Thus, \(-100\) is not a natural number.

Hence, the correct option is (D).

As we know,

Simple Interest \(=\frac{P \times R \times T}{100}\)

Where \(P=\) Principal

\(R=\) Rate of interest

\(T=\) time period

According to question,

\(4000=\frac{P \times 8 \times 5}{100} \)

\(\Rightarrow 400000=P \times 8 \times 5 \)

\(\Rightarrow P=\frac{400000}{40} \)

\(\therefore P=\) Rs. \( 10000\)

So, she took Rs. \(10000\) as loan.

Hence, the correct option is (A).

Given,

Cost price of \(25\) saris \(=\) Rs \(11000\)

Selling price of \(1\) sari \(=\) Rs \(460\)

\(\therefore\) Selling price of \(25\) saris \(=25 \times 460=\) Rs \(11500\)

Since selling price is more than cost price, so there is a profit.

Profit \(=\) Selling price \(-\) cost price

\(=11500-11000\)

\(=\) Rs \(500\)

So, Kantabai made a profit of Rs \(500\) in this transaction.

Hence, the correct option is (B).

Let the number to be added to \(26.67\) to get 30 is \(x\).

According to question,

\(26.67+x=30 \)

\(\Rightarrow x=30-26.67 \)

\(\Rightarrow x=03.33\)

So, \(3.33\) is to be added to \(26.67\) to become \(30\).

Hence, the correct option is (B).

Given,

Cost price of 1 quintal of onions \(=\) Rs \(2000\)

As we know,

\(1\) quintal \(=100 kg\)

Selling price of \(1 kg\) of onions \(=\) Rs \(18\)

\(\therefore\) Selling price of \(100 kg\) (or \(1\) quintal) of onions \(=18 \times 100=\) Rs \(1800\)

Since selling price is less than cost price, so there is a loss.

Loss \(=\) Cost price \(-\) Selling price

\(=2000-1800\)

\(=\) Rs \(200\)

So, Sharad incurred a loss of Rs \(200\) in this transaction.

Hence, the correct option is (B).

Given,

Principal \((P)=\) Rs. \(78000\), Rate \((R)=\frac{77}{5} \%\) p.a and \(T=\frac{9}{12}\)

years \(=\frac{3}{4}\) years

As we know,

Simple interest \(=\frac{(P \times R \times T)}{100}\)

\(=\frac{\left(78000 \times \frac{77}{5} \times \frac{3}{4}\right)}{100} \)

\(=\frac{3900 \times 77 \times 3}{100} \)

\(=\frac{900900}{100} \)

\(=\) Rs.\( 9009\)

Hence, the correct option is (D).

Factor of \(88=1,2,4,8,11,22,44,88\)

So, \(88\) has \(8\) factors.

Hence, the correct option is (A).