ICSE ICSE Class 7 - CISCE Question Bank Solutions for Mathematics

Two numbers are in the ratio 5: 7. Their difference is 10. Find the numbers.

In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.

Two numbers are in the ratio 10: 11. Their sum is 168. Find the numbers.

A line is divided into two parts in the ratio 2.5 : 1.3. If the smaller one is 35.1 cm, find the length of the line.

In a class, the ratio of boys to the girls is 7:8. What part of the whole class are girls?

In the given figure, angle ACP = ∠BDP = 90°, AC = 12 m, BD = 9 m and PA= PB = 15 m. Find:
(i) CP
(ii) PD
(iii) CD

The population of the town is 180,000, out of which males are `1/3` of the whole population. Find the number of females. Also, find the ratio of the number of females to the whole population.

Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is metal B. Find the ratio between:

1. the weights of metals A and B in the alloy.
2. the weight of metal B and the weight of the alloy.

In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm

The ages of two boys A and B are 6 years 8 months and 7 years 4 months respectively. Divide Rs. 3,150 in the ratio of their ages.

In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm

Three persons start a business and spend Rs. 25,000; Rs. 15,000 atid Rs. 40,000 respectively. Find the share of each out of a profit of Rs. 14,400 in a year

A plot of land, 600 sq m in area, is divided between two persons such that the first person gets three-fifth of what the second gets. Find the share of each.

Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm

Two poles of different heights are standing vertically on a horizontal field. At a particular time, the ratio between the lengths of their shadows is 2 :3. If the height of the smaller pole is 7.5 m, find the height of the other pole.

Two numbers are in the ratio 4 : 7. If their L.C.M. is 168, find the numbers.

In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :
(i) AC
(ii) CD

₹ 300 is divided between A and B in such a way that A gets half of B. Find:

1. the ratio between the shares of A and B. 
2. the share of A and the share of B.

In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.

The ratio between two numbers is 5 : 9. Find the numbers, if their H.C.F. is 16.