EN हिं

NCERT Solutions for Class 7th Maths Chapter 7 Solving Problems — In-text Questions

Book page 175 – 177 Updated on2026-09-19

Q1.
Example 8: Madhubanti wants to organise a party. She decides to buy snacks for the party from the chaat shop in town. Each plate of snacks costs ₹25. The shop charges an additional fixed amount of ₹50 to deliver the snacks to Madhubanti's house. There are 5 members in Madhubanti's family, including herself. Her parents tell her she can spend ₹500 on this party. How many friends can she invite to the party if she wants to give a plate of snacks to each person, including her family and friends?
Answer

She can invite 13 friends.

Let p be the total number of people at the party, family and friends together.

Cost = 25p + 50  (₹25 per plate, plus ₹50 delivery)
This must be ₹500, so
25p + 50 = 500
25p = 500 − 50 = 450
p = 450 ÷ 25 = 18 people

Of these 18, five are her family, so
friends = 18 − 5 = 13

Fatima reached the same answer without algebra: take the ₹50 delivery out of ₹500 first, leaving ₹450 for snacks; ₹450 ÷ ₹25 = 18 plates; 18 − 5 = 13 friends.

Why it happens: the ₹50 is a fixed charge — it is paid once, however many plates are bought. The ₹25 is a rate — it is paid for each plate. So the total cost is "rate × number + fixed", which is 25p + 50. Removing the fixed part from both sides is what makes the rest a simple division.
Check it yourself: 18 plates cost 18 × 25 = ₹450, plus ₹50 delivery = ₹500 exactly. ✓
Q2.
Srikanth decided to represent the unknown quantity of the total number of friends Madhubanthi can invite as f. What will be the cost in this case?
Answer

Cost = 25 (f + 5), and solving gives f = 13 — the same answer.

If f friends come, the number of plates is f + 5 (the 5 family members too).
Cost of snacks = 25 (f + 5)

Madhubanti has ₹450 for snacks after the ₹50 delivery is paid, so
25 (f + 5) = 450
f + 5 = 450 ÷ 25 = 18  (divide both sides by 25)
f = 18 − 5 = 13
Why it happens: Mahesh named the total number of people and Srikanth named the number of friends. Different unknowns give different-looking equations — 25p + 50 = 500 and 25(f + 5) = 450 — but they describe the same party, so they must agree. Note that p and f are linked by p = f + 5, and 18 = 13 + 5. ✓
Tip: when a bracket is multiplied by a number that divides the other side exactly, divide first. Here dividing by 25 was far quicker than opening 25(f + 5) into 25f + 125.
Q3.
Example 9: Two friends want to save money. Jahnavi starts with an initial amount of ₹4000, and in addition, saves ₹650 per month. Sunita starts with ₹5050 and saves ₹500 per month. After how many months will they have the same amount of money?
Answer

After 7 months.

Let m be the number of months.

Jahnavi's savings after m months = 4000 + 650m
Sunita's savings after m months = 5050 + 500m

They are equal, so
4000 + 650m = 5050 + 500m
4000 + 650m − 500m = 5050  (subtract 500m from both sides)
4000 + 150m = 5050
150m = 5050 − 4000  (subtract 4000 from both sides)
150m = 1050
m = 1050 ÷ 150 = 7
Why it happens: Sunita begins ₹1050 ahead, but Jahnavi saves ₹150 more every month. So Jahnavi closes the gap at ₹150 a month, and 1050 ÷ 150 = 7 months to close it completely. The algebra does exactly this arithmetic, but it finds the two numbers 1050 and 150 for you.
Tip: subtracting 500m rather than 650m keeps the coefficient of m positive, which makes the last division easier.
Q4.
Check the answer. [For Example 9, m = 7 months.]
Answer

The check works out — both have ₹8550 after 7 months.

Jahnavi = 4000 + 650 × 7 = 4000 + 4550 = ₹8550
Sunita = 5050 + 500 × 7 = 5050 + 3500 = ₹8550
The two amounts are equal, so m = 7 is correct.
MonthJahnavi (₹)Sunita (₹)Gap (₹)
Start400050501050
146505550900
253006050750
679008050150
7855085500
Why it happens: the gap shrinks by exactly ₹150 each month — 1050, 900, 750, … , 150, 0. It reaches zero for the first time in month 7, and after that Jahnavi is ahead. The table and the equation tell the same story.
Was this helpful?