Number System — Exercise 1(B)

Population of a city was 3,54,976 in the year 2014. In the year 2015, it increased by 68,438. What was the population of the city at the end of the year 2015?

Answer

Population in the year 2014 = 3,54,976.

Increase in the year 2015 = 68,438.

Population at the end of 2015 = 3,54,976 + 68,438.

$\begin{array}{rr} & 3{,}54{,}976 \\ + & 68{,}438 \\ \hline & 4{,}23{,}414 \end{array}$

Hence, the population of the city at the end of the year 2015 = 4,23,414.

A = 7,43,000 and B = 8,00,100. Which is greater A or B? And by how much?

Answer

Both A and B have an equal number of digits. Comparing them at the lakhs place, B has 8 and A has 7.

Since 8 > 7, B is greater than A.

Difference = B - A = 8,00,100 - 7,43,000.

$\begin{array}{rr} & 8{,}00{,}100 \\ - & 7{,}43{,}000 \\ \hline & 57{,}100 \end{array}$

Hence, B is greater than A by 57,100.

A notebook has 56 pages. How many pages will 5326 such notebooks have?

Answer

Number of pages in one notebook = 56.

Number of pages in 5326 notebooks = 56 × 5326.

$\begin{array}{rr} & 5{,}326 \\ \times & 56 \\ \hline & 31{,}956 \\ & 2{,}66{,}300 \\ \hline & 2{,}98{,}256 \end{array}$

Hence, 5326 notebooks will have 2,98,256 pages.

A person has 75,000 sheets of paper. If each sheet makes 8 pages of a notebook, how many notebooks of 200 pages can be made using the above sheets?

Answer

Number of sheets = 75,000.

Total number of pages obtained = 8 × 75,000.

$\begin{array}{rr} & 75{,}000 \\ \times & 8 \\ \hline & 6{,}00{,}000 \end{array}$

Number of pages in one notebook = 200.

Number of notebooks made = 6,00,000 ÷ 200.

$\begin{array}{l} 200\overline{\smash{\big)}\phantom{.}600000\smash{\big(}}3000 \\ \phantom{+()}\underline{-600} \\ \phantom{++))}\phantom{000}000 \end{array}$

Hence, 3000 notebooks of 200 pages can be made.

Add 1,76,209 ; 4,50,923 and 44,83,947.

Answer

Required sum = 1,76,209 + 4,50,923 + 44,83,947.

$\begin{array}{rr} & 1{,}76{,}209 \\ & 4{,}50{,}923 \\ + & 44{,}83{,}947 \\ \hline & 51{,}11{,}079 \end{array}$

Hence, the required sum = 51,11,079.

A cricket player has scored 7,849 runs so far in test matches. He wishes to complete 10,000 runs; how many more runs does he need?

Answer

Runs to be completed = 10,000.

Runs already scored = 7,849.

Runs needed = 10,000 - 7,849.

$\begin{array}{rr} & 10{,}000 \\ - & 7{,}849 \\ \hline & 2{,}151 \end{array}$

Hence, the player needs 2151 more runs.

In an election two candidates A and B are the only contestants. If candidate A scored 9,32,567 votes and candidate B scored 9,00,235 votes, by how much margin did A win or loose the election?

Answer

Votes scored by A = 9,32,567.

Votes scored by B = 9,00,235.

Since 9,32,567 > 9,00,235, candidate A won the election.

Margin = 9,32,567 - 9,00,235.

$\begin{array}{rr} & 9{,}32{,}567 \\ - & 9{,}00{,}235 \\ \hline & 32{,}332 \end{array}$

Hence, A won the election by 32332 votes.

Find the difference between the largest and the smallest five digit numbers that can be formed using the digits 5, 1, 6, 3 and 2 without repeating any digit.

Answer

Largest five-digit number (digits in descending order) = 65321.

Smallest five-digit number (digits in ascending order) = 12356.

Required difference = 65321 - 12356.

$\begin{array}{rr} & 65{,}321 \\ - & 12{,}356 \\ \hline & 52{,}965 \end{array}$

Hence, the required difference = 52965.

A man has ₹ 1,57,184 with him. He placed an order for purchasing 80 articles at ₹ 125 each. How much money will remain with him after the purchase?

Answer

Money that man has = ₹ 1,57,184.

Cost of 80 articles = 80 × ₹ 125.

$\begin{array}{rr} & 125 \\ \times & 80 \\ \hline & 10{,}000 \end{array}$

Remaining Money = ₹ 1,57,184 - ₹ 10,000.

$\begin{array}{rr} & 1{,}57{,}184 \\ - & 10{,}000 \\ \hline & 1{,}47{,}184 \end{array}$

Hence, ₹ 1,47,184 will remain with him after the purchase.

A student multiplied 8,035 by 87 instead of multiplying by 78. By how much was his answer greater than or less than the correct answer?

Answer

The student's answer = 8,035 × 87.

The correct answer = 8,035 × 78.

Difference = 8,035 × 87 - 8,035 × 78

= 8,035 × (87 - 78)

= 8,035 × 9.

$\begin{array}{rr} & 8{,}035 \\ \times & 9 \\ \hline & 72{,}315 \end{array}$

Since 87 > 78, the student's answer was greater than the correct answer.

Hence, his answer was greater than the correct answer by 72,315.

Mohani has 30 m cloth and she wants to make some shirts for her son. If each shirt requires 2 m 30 cm cloth, how many shirts, in all, can be made and how much length of the cloth will be left?

Answer

Total length of cloth = 30 m = 3000 cm.

Cloth required for one shirt = 2 m 30 cm = 230 cm.

Number of shirts = 3000 ÷ 230.

$\begin{array}{l} 230\overline{\smash{\big)}\phantom{.}3000\smash{\big(}}13 \\ \phantom{+()}\underline{-230} \\ \phantom{++))}\phantom{0}700 \\ \phantom{+()}\phantom{0}\underline{-690} \\ \phantom{230,\big),}\phantom{00}10 \end{array}$

So, 13 shirts can be made and 10 cm of cloth is left as remainder.

Cloth used for 13 shirts = 13 × 230 cm.

$\begin{array}{rr} & 230 \\ \times & 13 \\ \hline & 690 \\ & 2{,}300 \\ \hline & 2{,}990 \end{array}$

Cloth left = 3000 cm - 2990 cm.

$\begin{array}{rr} & 3{,}000 \\ - & 2{,}990 \\ \hline & 10 \end{array}$

Hence, 13 shirts can be made and 10 cm of cloth will be left.

The distance between two places A and B is 3 km 760 m. A boy travels from A to B and then B to A every day. How much distance does he travel in 8 days?

Answer

Distance between A and B = 3 km 760 m = 3760 m.

Distance travelled in one day (A to B and B to A) = 2 × 3760 m.

$\begin{array}{rr} & 3{,}760 \\ \times & 2 \\ \hline & 7{,}520 \end{array}$

Distance travelled in 8 days = 8 × 7520 m.

$\begin{array}{rr} & 7{,}520 \\ \times & 8 \\ \hline & 60{,}160 \end{array}$

60160 m = $\dfrac{60160}{1000}$ = 60.160 km.

Hence, the boy travels 60.160 km in 8 days.

An oil-tin contains 6 litre 60 ml oil. How many identical bottles can this oil fill, if the capacity of each bottle is 30 ml?

Answer

Quantity of oil = 6 litre 60 ml = 6060 ml (since 1 litre = 1000 ml).

Capacity of each bottle = 30 ml.

Number of bottles = 6060 ÷ 30.

$\begin{array}{l} 30\overline{\smash{\big)}\phantom{0}6060\smash{\big(}}202 \\ \phantom{())}\underline{-60} \\ \phantom{++}\phantom{00}60 \\ \phantom{+)}\phantom{00}\underline{-60} \\ \phantom{30,\big),}\phantom{000}0 \end{array}$

Hence, 202 identical bottles can be filled.

The sale receipt of a company in a certain year was ₹ 83,73,540. In the following year, it decreased by ₹ 7,84,670.

(i) What was the sale receipt of the company during the following year?

(ii) What was the total sale receipt of the company during these two years?

Answer

(i) Sale receipt in the first year = ₹ 83,73,540.

Decrease in the following year = ₹ 7,84,670.

Sale receipt in the following year = ₹ 83,73,540 - ₹ 7,84,670.

$\begin{array}{rr} & 83{,}73{,}540 \\ - & 7{,}84{,}670 \\ \hline & 75{,}88{,}870 \end{array}$

Hence, the sale receipt during the following year = ₹ 75,88,870.

(ii) Total sale receipt during the two years = ₹ 83,73,540 + ₹ 75,88,870.

$\begin{array}{rr} & 83{,}73{,}540 \\ + & 75{,}88{,}870 \\ \hline & 1{,}59{,}62{,}410 \end{array}$

Hence, the total sale receipt during these two years = ₹ 1,59,62,410.

A number exceeds 8,59,470 by 3,00,999. What is the number?

Answer

The required number = 8,59,470 + 3,00,999.

$\begin{array}{rr} & 8{,}59{,}470 \\ + & 3{,}00{,}999 \\ \hline & 11{,}60{,}469 \end{array}$

Hence, the required number = 11,60,469.