(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

Two positive numbers are in the ratio 3: 4 and the sum of their squares is 1225. Find the numbers. 

Two numbers are in the ratio 5 : 7 and the difference of their squares is 600. Find the numbers. 

What quantity must be subtracted from each term of the ratio 39 : 89 to make it equal to 2 : 5 ? 

What quantity must be added to each term of the ratio 19 : 51 to make it equal to 3 : 7 ? 

What quantity must be added to each term of the ratio (p + q) : (p - q) to make it equal to (p + q)² : (p - q)² ?

If (3x-4) : (2x+5) is the duplicate ratio of 3 : 4 , find x. 

If (5x+3) : (3x+ 1) is the triplicate ratio of 4 : 3 ,  find x. 

If r² = pq , show that p : q is the duplicate ratio of (p+r) : ( q+r) 

A sum of money Is divided in the ratio 2 : 3. If the larger portion is Rs 7,47,300. find the sum distributed. 

Divide a number into two parts in the ratio 5:7 so that smaller part is 60. Find the number. 

A bag contains Rs 1800 in the form of Rs 1 , Rs 2 and Rs 5 ooins. The ratio of the number of the respective coins is 3: 7: 11. Find the total number of ooi ns in the bag.

The present age of two persons are in the ratio 4: 3. Nine years hence their ages will be in the ratio 23: 18. Find their present ages. 

The ratio of the pocket money saved by a boy and his sister is 5:4. If the brother saves Rs 100 more, how much more should the sister save in order to keep the ratio of their savings unchanged ? 

A cistern of milk caitains a mixture of milk and water in the ratio of 11 :4. If the cistern contains 60 litres of milk, how much more water must be added to make the 
ratio of milk to water as 11:6 ?

In an examination the ratio of the number of suo:essful candidates to unsuccessful candidates is 7:5. Had 30 more appeared and 10 more passed, the ratio of successful candidates to unsuccessful candidates would have been 4:3. Find the number of candidates who appeared in the examination originally. 

If `"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c")` , then prove that each ratio is equal to the ratio of `("x + y+z")/("a + b + c")`

If `"a"/("b + c") = "b"/("c + a") = "c"/("a + b")` , then prove that a(b - c) + b(c-a) + c (a - b) = 0

If x = `"pab"/("a + b")`, then prove that `("x + pa")/("x - pa") + ("x + pb")/("x - pb") = (2("a"^2 - "b"^2))/"ab"`

Show that the value of x is 11, when `("x"^3 + "3x")/(3"x"^2 + 1) = 341/91`

Classify the following rnatrix : 

`|(2,1),(0 , 6),(8 , 7) |`