Exam practice

Every question from the end of every unit, with hints and answers to open. After you check an answer, mark how you did, and come back to the ones you didn’t get.

75 questions

Unit 4 · Household Arithmetic

Exercise 4.1

Question 1

How many units were used in Mangsir?

Answer

3593 − 3528 = 65 units.

In which month did the house use the most electricity, and in which the least?

Answer

Mangsir 65, Poush 3700 − 3593 = 107, Magh 3904 − 3700 = 204, Falgun 3980 − 3904 = 76 units.
Most in Magh (204 units), least in Mangsir (65 units). (Kartik’s use can’t be found: the reading before it isn’t given.)

Question 2

Present reading 2575, previous reading 2472, a 5 A meter; paid on day 4 after the reading.

Answer

Units = 2575 − 2472 = 103: the 101–250 block, minimum Rs 100.
Energy = 60 + 65 + 160 + 53 × 9.50 = 285 + 503.50 = 788.50; bill = 888.50.
Day 4: 2% off, 888.50 × 0.98 = 870.73. Rs 870.73.

Present reading 3036, previous reading 2831, a 15 A meter; paid on day 41.

Answer

Units = 205: minimum Rs 125.
Energy = 20 × 4 + 10 × 6.50 + 20 × 8 + 155 × 9.50 = 80 + 65 + 160 + 1472.50 = 1777.50; bill = 1902.50.
Day 41: 25% fine, 1902.50 × 1.25 = 2378.125. Rs 2,378.13.

Present reading 3603, previous reading 3294, a 30 A meter; paid on day 39.

Answer

Units = 309: over 250, minimum Rs 200.
Energy = 20 × 5 + 65 + 160 + 200 × 9.50 + 59 × 11 = 100 + 65 + 160 + 1900 + 649 = 2874; bill = 3074.
Day 39: 10% fine, 3074 × 1.10 = Rs 3,381.40.

Present reading 4311, previous reading 3944, a 60 A meter; paid on day 14.

Answer

Units = 367: over 250, minimum Rs 250.
Energy = 20 × 6 + 65 + 160 + 1900 + 117 × 11 = 120 + 65 + 160 + 1900 + 1287 = 3532; bill = 3782.
Day 14: as billed. Rs 3,782.

Present reading 5555, previous reading 5107, a 30 A meter; paid on day 17.

Answer

Units = 448: minimum Rs 200.
Energy = 100 + 65 + 160 + 1900 + 198 × 11 = 2225 + 2178 = 4403; bill = 4603.
Day 17: 5% fine, 4603 × 1.05 = Rs 4,833.15.

Present reading 6452, previous reading 6443, a 5 A meter; paid on day 57.

Answer

Units = 9: 20 or less on 5 A, so Rs 30 only.
Day 57: 25% fine, 30 × 1.25 = Rs 37.50.

Exercise 4.2

Question 1

How much does she pay for the 50% sewerage service that month?

Answer

Units = 28. Water charge = 100 + 18 × 32 = 676. Sewerage $= \frac{50}{100} \times 676 =$ Rs 338.

What is the whole bill?

Answer

676 + 338 = Rs 1,014.

How much does she pay if she pays in the first or second month?

Answer

3% off: 1014 × 0.97 = Rs 983.58.

How much does she pay if she pays in the third month?

Answer

The bill as it is: Rs 1,014.

Question 2

What is the month’s bill, sewerage included?

Answer

Water charge = 10950 + (423 − 155) × 71 = 10950 + 19028 = 29978.
Bill = 29978 × 1.5 = Rs 44,967.

If the bill is paid in the fifth month, what is the fine, and what is paid in all?

Answer

20% fine $= \frac{20}{100} \times 44967 = 8993.40$ .
A fine of Rs 8,993.40; Rs 53,960.40 in all.

Exercise 4.3

Question 1

How many calls were made in Baishakh?

Answer

4444 − 3992 = 452 calls.

What is the TC?

Answer

200 + (452 − 175) × 1 = 200 + 277 = Rs 477.

Find the 13% TSC and the 13% VAT.

Answer

TSC $= \frac{13}{100} \times 477 =$ Rs 62.01.
VAT $= \frac{13}{100} \times (477 + 62.01) = \frac{13}{100} \times 539.01 =$ Rs 70.07.

What is the total with VAT?

Answer

477 + 62.01 + 70.07 = Rs 609.08.

Question 2

550 calls

Answer

TC = 200 + 375 = 575; total = 575 × 1.13 × 1.13 = Rs 734.22.

695 calls

Answer

TC = 200 + 520 = 720; total = 720 × 1.2769 = Rs 919.37.

793 calls

Answer

TC = 200 + 618 = 818; total = 818 × 1.2769 = Rs 1,044.50.

Question 3

Rs 275

Answer

175 + (275 − 200) = 250 calls.

Rs 695

Answer

175 + 495 = 670 calls.

Rs 890

Answer

175 + 690 = 865 calls.

Question 4

The first 175 calls cost Rs 200 and each call after that Re 1. With 10% TSC and 13% VAT the month’s total is Rs 696.08. How many calls were made?

Answer

Total = TC × 1.10 × 1.13 = TC × 1.243, so TC = 696.08 ÷ 1.243 = 560.
Calls = 175 + (560 − 200) = 535 calls.
Check: 560 × 1.10 = 616, 616 × 1.13 = 696.08. ✓

Question 5

An NT postpaid connection has a monthly rental of Rs 300. 13% TSC is added to it, then 13% VAT, then 2% OT on the total. What is the least a postpaid user pays in a month?

Answer

300 × 1.13 × 1.13 × 1.02 = 390.73. Rs 390.73.

Exercise 4.4

Question 1

Shreenath took a taxi 9 km from Baneshwar to Bhaktapur by day: Rs 14 to start, then Rs 7.80 for each 200 m, and 6 minutes of waiting at Rs 7.80 for 2 minutes. What was the fare?

Answer

14 + 39 × 9 + 3.90 × 6 = 14 + 351 + 23.40 = Rs 388.40.

Question 2

Shristi took a taxi 18 km from Jagati, Bhaktapur to Sanepa, Lalitpur by day, with 20 minutes of waiting, at the same rates. What did she pay?

Answer

14 + 39 × 18 + 3.90 × 20 = 14 + 702 + 78 = Rs 794.

Question 3

6 km at 8 AM, 15 minutes of waiting

Answer

Day: 14 + 39 × 6 + 3.90 × 15 = 14 + 234 + 58.50 = Rs 306.50.

15 km at 3:30 PM, 10 minutes of waiting

Answer

Day: 14 + 39 × 15 + 39 = 14 + 585 + 39 = Rs 638.

7.5 km at 11 PM, no waiting

Answer

Night: 21 + 58.50 × 7.5 = 21 + 438.75 = Rs 459.75.

8.75 km at 4 AM, 7 minutes of waiting

Answer

Night: 21 + 58.50 × 8.75 + 5.85 × 7 = 21 + 511.875 + 40.95 = 573.825. Rs 573.83.

Question 4

Samyog paid Rs 228.50 for a day ride with 10 minutes of waiting: Rs 14 to start, Rs 7.80 for each 200 m, and Rs 7.80 for 2 minutes of waiting. How far did he travel?

Answer

Start and waiting: 14 + 3.90 × 10 = 53. For the distance: 228.50 − 53 = 175.50.
Distance = 175.50 ÷ 39 = 4.5. 4.5 km (4,500 m).

Question 5

Phulmaya paid Rs 1,027.20 for a night ride with 12 minutes of waiting: Rs 21 to start, Rs 11.70 for each 200 m, and Rs 11.70 for 2 minutes of waiting. How far did she travel?

Answer

Start and waiting: 21 + 5.85 × 12 = 21 + 70.20 = 91.20. For the distance: 1027.20 − 91.20 = 936.
Distance = 936 ÷ 58.50 = 16. 16 km.

Miscellaneous exercise

Question 1

A person earning Rs 7 lakh a year pays income tax of 1% up to Rs 4,50,000 and 10% on the rest. How much income tax is paid?

Answer

$\frac{1}{100} \times 450000 + \frac{10}{100} \times 250000 = 4500 + 25000 =$ Rs 29,500.

Question 2

A person earning Rs 4,60,000 a year pays Rs 5,500 income tax. If the rate is 1% up to Rs 4,50,000, what is the rate on the rest?

Answer

Tax on the first Rs 4,50,000 = 4500; on the other Rs 10,000 it is 5500 − 4500 = 1000.
Rate $= \frac{1000}{10000} \times 100\% =$ 10%.

Question 3

Rs 7,60,000

Answer

$\frac{2.5}{100} \times 760000 =$ Rs 19,000.

Rs 15,70,500

Answer

$25000 + \frac{4}{100} \times 570500 = 25000 + 22820 =$ Rs 47,820.

Rs 23,75,600

Answer

$25000 + 40000 + \frac{5.25}{100} \times 375600 = 65000 + 19719 =$ Rs 84,719.

Rs 55,75,000

Answer

$25000 + 40000 + 105000 + \frac{12.75}{100} \times 1575000 = 170000 + 200812.50 =$ Rs 3,70,812.50.

Question 4

What is the simple interest on Rs 50,000 for 1 year at 2 paisa per Rs 3 per month? If 5% tax is taken from the interest, what is the interest left?

Answer

2 paisa on Rs 3 a month is $\frac{0.02}{3} \times 12 \times 100\% = 8\%$ a year.
Interest $= \frac{8}{100} \times 50000 =$ Rs 4,000; tax = 200; left Rs 3,800.

Question 5

How much does the customer pay?

Answer

10000 × 1.13 = Rs 11,300.

What percentage profit did the shopkeeper make?

Answer

Profit = 10000 − 7520 = 2480; $\frac{2480}{7520} \times 100\% =$ 32.98%.

Had it been sold at a 30% discount on the marked price, what would the price with VAT have been?

Answer

10000 × 0.70 = 7000; with VAT 7000 × 1.13 = Rs 7,910.

Would the shopkeeper then have made a profit or a loss, and of what percentage?

Answer

7000 < 7520: a loss of Rs 520; $\frac{520}{7520} \times 100\% =$ a loss of 6.91%.

Question 6

A laptop bought for Rs 1,50,000 is sold at a profit of 10%. What is its price with 13% VAT?

Answer

150000 × 1.10 = 165000; 165000 × 1.13 = Rs 1,86,450.

Question 7

An item is sold for Rs 9,040 after a 20% discount and with 13% VAT. How much was the discount?

Answer

Price before VAT = 9040 ÷ 1.13 = 8000; this is 80% of the marked price, so the marked price = 8000 ÷ 0.80 = 10000.
Discount = 10000 − 8000 = Rs 2,000.

Question 8

What did the dealer pay the importer without VAT?

Answer

22600 ÷ 1.13 = Rs 20,000.

What profit did the retailer make?

Answer

The retailer bought for 25990 ÷ 1.13 = 23000 and sold for 28250 ÷ 1.13 = 25000, both without VAT: profit Rs 2,000.

How much VAT should reach the government on the computer in all?

Answer

13% of the last price without VAT: $\frac{13}{100} \times 25000 =$ Rs 3,250.

How much VAT should the retailer deposit with the government?

Answer

VAT collected 3250 − VAT paid to the dealer 2990 = Rs 260.

Question 9

A sales manager’s monthly salary is Rs 22,000, and 0.75% commission on the month’s sales is added to it. If a month’s sales are Rs 6,24,000, what is the income? By what percentage of the salary does the commission add to it?

Answer

Commission $= \frac{0.75}{100} \times 624000 = 4680$ ; income = 22000 + 4680 = Rs 26,680.
$\frac{4680}{22000} \times 100\% =$ 21.27% of the salary.

Question 10

10.

A house owner gives an agent 3% of the monthly rent for renting out the house. If the rent is Rs 75,000 a month, how much does the agent receive in a year?

Answer

$\frac{3}{100} \times 75000 \times 12 = 2250 \times 12 =$ Rs 27,000.

Question 11

11.

Rohan received Rs 1 crore 28 lakh 25 thousand for his house after paying the agent 5% commission. What was the selling price?

Answer

He kept 95% of the price: 12825000 ÷ 0.95 = Rs 1,35,00,000.

Question 12

12.

25% of a company’s profit is Rs 1,50,000. It shares 65% of the whole profit equally among its 15 employees as a bonus. How much does each receive?

Answer

Profit = 150000 ÷ 0.25 = 600000; bonus $= \frac{65}{100} \times 600000 = 390000$ ; each = 390000 ÷ 15 = Rs 26,000.

Question 13

13.

A bank shared 55% of a year’s profit as a bonus among its 275 employees, Rs 65,000 each. What was its profit?

Answer

Bonus = 275 × 65000 = 17875000; profit = 17875000 ÷ 0.55 = Rs 3,25,00,000.

Question 14

14.

A cement company has 3,50,000 shares of Rs 100. Chiring has 250 of them from its IPO. The company makes a profit of Rs 9,00,00,000 and pays 40% of it as a cash dividend. How much does Chiring get?

Answer

Dividend $= \frac{40}{100} \times 90000000 = 36000000$ ; per share $= 36000000 \div 350000 = 102.857…$ ; Chiring’s $= \frac{36000000}{350000} \times 250 =$ Rs 25,714.29.
(Here 40% is of the profit, as in Unit 3. A 40% dividend on the face value would be only Rs 40 a share, Rs 10,000.)

Question 15

How many units were used in each month from Jestha to Ashoj?

Answer

Jestha 45, Ashar 25, Shrawan 15, Bhadra 27, Ashoj 42 units (154 in all).

Which month’s bill is the highest, and how much is it?

Answer

Jestha: minimum Rs 50; energy 60 + 65 + 15 × 8 = 245. Jestha, Rs 295.

Which month’s bill is the lowest, and how much is it?

Answer

Shrawan, 15 units: 20 or less on 5 A. Shrawan, Rs 30.

How much is paid if Jestha’s bill is paid on 13 Ashar?

Answer

Day 13 after the reading: as billed, Rs 295.

How much is paid if Ashar’s bill is paid on 27 Shrawan?

Answer

Ashar, 25 units: 50 + 60 + 5 × 6.50 = 142.50. Day 27: 5% fine, 142.50 × 1.05 = 149.625. Rs 149.63.

How much is paid if Ashoj’s bill is paid on 5 Kartik?

Answer

Ashoj, 42 units: 50 + 60 + 65 + 12 × 8 = 271. Day 5: 2% off, 271 × 0.98 = Rs 265.58.

Question 16

16.

A hotel used 58,000 liters of water through a ¾ inch pipe. With 50% sewerage, how much does it pay if it pays in the fourth month after the bill is handed out?

Answer

58 units: 1910 + (58 − 27) × 71 = 1910 + 2201 = 4111; with sewerage 4111 × 1.5 = 6166.50.
Fourth month, 10% fine: 6166.50 × 1.10 = Rs 6,783.15.

Question 17

275 calls

Answer

TC = 300; 300 × 1.13 × 1.13 = Rs 383.07.

325 calls

Answer

TC = 350; 350 × 1.2769 = 446.915. Rs 446.92.

469 calls

Answer

TC = 494; 494 × 1.2769 = Rs 630.79.

Question 18

Rs 766.14

Answer

TC = 766.14 ÷ 1.2769 = 600; calls = 175 + 400 = 575.

Rs 893.83

Answer

TC = 700; 675 calls.

Rs 1,021.52

Answer

TC = 800; 775 calls.

Rs 1,149.21

Answer

TC = 900; 875 calls.

Question 19

4 km

Answer

14 + 39 × 4 = Rs 170.

9 km

Answer

14 + 351 = Rs 365.

13 km

Answer

14 + 507 = Rs 521.

15 km

Answer

14 + 585 = Rs 599.