EN हिं

NCERT Solutions for Class 5th Maths Chapter 6 The last set of word problems — Let Us Solve

Book page 91 Updated on2026-09-19

Q1.
Mala went to a book exhibition and bought 18 books. The shop was selling 3 books for ₹150. After buying the books, she still had ₹20 left. How much money did Mala have at the beginning?
Answer

Mala had ₹920 at the beginning.

The books are sold in sets of 3, so first find how many sets she bought.

Step 1. Number of sets = 18 ÷ 3 = 6 sets
Step 2. Cost of one set = ₹150
Step 3. Cost of 6 sets = 6 × 150
   6 × 15 = 90, so 6 × 150 = ₹900
Step 4. She still had ₹20 left over.
Step 5. Money at the start = 900 + 20 = ₹920
Why we add the ₹20 at the end: The money she started with was used up in two ways — some was spent on books, and some stayed in her purse. Adding both back together gives what she began with.
Check it yourself: Start with ₹920. Take away ₹900 for the books. ₹20 is left ✓ And 6 sets of 3 books is 18 books ✓
Q2.
A village sports club organises a women's football tournament. They sold 57 tickets for ₹115 each. They had 3 teams joining the tournament, with each team paying a participation fee of ₹1,599. (a) How much money did the club collect in total from ticket sales and team participation fees?
Answer

The club collected ₹11,352 in all.

There are two sources of money, so work out each one and then add.

Money from tickets
Step 1. 57 tickets × ₹115 each
Step 2. 57 × 100 = 5,700
Step 3. 57 × 15 = 855
Step 4. 5,700 + 855 = ₹6,555
Money from participation fees
Step 1. 3 teams × ₹1,599 each
Step 2. Use the nearest multiple: 3 × 1,600 = 4,800
Step 3. That is ₹3 too much (one rupee per team).
Step 4. 4,800 − 3 = ₹4,797
Total collected
₹6,555 + ₹4,797 = ₹11,352
Check the tickets a second way: 57 × 115 = 115 × 57 = 115 × 50 + 115 × 7 = 5,750 + 805 = ₹6,555 ✓
Q3.
(b) The teams paid ₹1,750 in total to rent the football ground and ₹1,129 for food and water. What were the total expenses on renting the ground and food and water?
Answer

The total expenses were ₹2,879.

Step 1. Ground rent = ₹1,750
Step 2. Food and water = ₹1,129
Step 3. Add the ones: 0 + 9 = 9
Step 4. Add the tens: 50 + 20 = 70
Step 5. Add the hundreds: 700 + 100 = 800
Step 6. Add the thousands: 1,000 + 1,000 = 2,000
Step 7. Total = 2,000 + 800 + 70 + 9 = ₹2,879
Did you know? Comparing money in with money out is how any club or shop checks it is doing well. Here the club collected ₹11,352 and spent ₹2,879, so it kept 11,352 − 2,879 = ₹8,473 for the village.
Q4.
Ananya is watching Republic Day celebrations on the city's public ground. There are 12 rows of students sitting in front of her and 17 rows behind her. There are 18 students to her right and 22 students to her left. (a) How many rows of students are there in total? (b) How many students are there in Ananya's row? (c) What is the total number of students on the ground?
Answer

(a) 30 rows (b) 41 students (c) 1,230 students.

The important thing to remember is that Ananya herself must be counted — she is sitting in a row too.

(a) Total rows
Step 1. Rows in front = 12
Step 2. Rows behind = 17
Step 3. Ananya's own row = 1
Step 4. Total = 12 + 17 + 1 = 30 rows
(b) Students in Ananya's row
Step 1. Students to her right = 18
Step 2. Students to her left = 22
Step 3. Ananya herself = 1
Step 4. Total = 18 + 22 + 1 = 41 students
(c) Total students on the ground
Step 1. 30 rows, each with 41 students
Step 2. 30 × 41 = 30 × 40 + 30 × 1
Step 3. 1,200 + 30 = 1,230 students
12 rows in front (12 rows) 18 to her right 22 to her left 17 rows behind (17 rows) Ananya is the red dot. Her own row and her ownseat must be counted.
12 rows + Ananya's row + 17 rows = 30 rows. 18 + Ananya + 22 = 41 in her row.
Why we add 1 twice: "In front of her" does not include her. "Behind her" does not include her either. So her own row is a separate row. In the same way, the students to her right and left do not include her, so she is one extra person in her row.
Check it yourself: 30 × 41 should be a little more than 30 × 40 = 1,200. Our answer 1,230 is 30 more, which is exactly one extra student in each of the 30 rows ✓
Q5.
Multiply. (a) 67 × 78 (b) 34 × 56 (c) 45 × 263 (d) 86 × 542 (e) 432 × 107 (f) 310 × 120
Answer

All six products, each with a short method.

(a) 67 × 78 = 5,226
Step 1. 67 × 80 = 5,360
Step 2. That is two 67s too many: 2 × 67 = 134
Step 3. 5,360 − 134 = 5,226
(b) 34 × 56 = 1,904
Step 1. 34 × 50 = 1,700
Step 2. 34 × 6 = 204
Step 3. 1,700 + 204 = 1,904
(c) 45 × 263 = 11,835
Step 1. 263 × 40 = 10,520
Step 2. 263 × 5 = 1,315
Step 3. 10,520 + 1,315 = 11,835
(d) 86 × 542 = 46,612
Step 1. 542 × 80 = 43,360
Step 2. 542 × 6 = 3,252
Step 3. 43,360 + 3,252 = 46,612
(e) 432 × 107 = 46,224
Step 1. 432 × 100 = 43,200
Step 2. 432 × 7 = 3,024
Step 3. 43,200 + 3,024 = 46,224
(f) 310 × 120 = 37,200
Step 1. Set the zeros aside: 31 × 12 = 372
Step 2. One zero from 310 and one from 120 → two zeros
Step 3. Answer = 37,200
Check (c) with an estimate: 45 is about 50 and 263 is about 260, so expect around 50 × 260 = 13,000. Our 11,835 is in the right neighbourhood ✓
Q6.
If 67 × 67 = 4489, without multiplication find 67 × 68.
Answer

67 × 68 = 4,556.

  1. Compare the two questions. 67 × 67 has 67 groups of 67. 67 × 68 has 68 groups of 67.
  2. So there is one extra group. That group holds 67.
  3. Add it on. 4,489 + 67 = 4,556.
67 × 68 = 67 × 67 + 67
= 4,489 + 67
= 4,556
Check it if you like: 67 × 68 = 67 × 70 − 67 × 2 = 4,690 − 134 = 4,556 ✓
Q7.
If 99 × 100 = 9900, without multiplication find 99 × 99.
Answer

99 × 99 = 9,801.

  1. Compare the two questions. 99 × 100 has 100 groups of 99. 99 × 99 has only 99 groups of 99.
  2. So there is one group fewer. That group holds 99.
  3. Take it away. 9,900 − 99 = 9,801.
99 × 99 = 99 × 100 − 99
= 9,900 − 99
= 9,801
Why this is the nearest-multiple idea again: The whole chapter keeps returning to it. Jump to the friendly number, then step back by exactly the groups you added. Here the friendly number was 100 and the step back was one group of 99.
Try this: Use the same idea to find 999 × 999 from 999 × 1,000 = 999,000. Take away one 999 and you get 998,001.
Was this helpful?